Lifting Solutions To Perturbing Problems In C Algebras

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Lifting Solutions to Perturbing Problems in C*-algebras

Author : Terry A. Loring
Publisher : American Mathematical Soc.
ISBN 13 : 9780821871911
Total Pages : 180 pages
Book Rating : 4.8/5 (719 download)

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Book Synopsis Lifting Solutions to Perturbing Problems in C*-algebras by : Terry A. Loring

Download or read book Lifting Solutions to Perturbing Problems in C*-algebras written by Terry A. Loring and published by American Mathematical Soc.. This book was released on 1997-01-01 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The techniques of universal algebra are applied to the category of C*-algebras. An important difference, central to this book, is that one can consider approximate representations of relations and approximately commuting diagrams. Moreover, the highly algebraic approach does not exclude applications to very geometric C*-algebras. K-theory is avoided, but universal properties and stability properties of specific C*-algebras that have applications to K-theory are considered. Index theory arises naturally, and very concretely, as an obstruction to stability for almost commuting matrices. Multiplier algebras are studied in detail, both in the setting of rings and of C*-algebras. Recent results about extensions of C*-algebras are discussed, including a result linking amalgamated products with the Busby/Hochshild theory.

Lifting Solutions to Perturbing Problems in $C*$-Algebras

Author : Terry A. Loring
Publisher : American Mathematical Soc.
ISBN 13 : 0821806025
Total Pages : 177 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lifting Solutions to Perturbing Problems in $C*$-Algebras by : Terry A. Loring

Download or read book Lifting Solutions to Perturbing Problems in $C*$-Algebras written by Terry A. Loring and published by American Mathematical Soc.. This book was released on 1997 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nature of C]*-algebras is such that one cannot study perturbation without also studying the theory of lifting and the theory of extenstions. Approximation questions involving representations of relations in matrices and C]*-algebras are the central focus of this volume. A variety of approximation techniques are unified by translating them into lifting problems: from classical questions about transivity of algebras of operators on Hilbert spaces to recent results in linear algebra. One chapter is devoted to Lin's theorem on approximating almost normal matrices by normal matrices. The techniques of universal algebra are applied to the category of C]*-algebras. An important difference, central to this book, is that one can consider approximate representations of relations and approximately commuting diagrams. Moreover, the highly algebraic approach does not exclude applications to very geometric C]*-algebras. K theory is avoided, but universal properties and stability properties of specific C]*-algebras that have applications to K-theory are considered. Index theory arises naturally, and very concretely, as an obstruction to stability for almost commuting matrices. Multiplier algebras are studied in detail, both in the setting of rings and of C]*-algebras. Recent results about extensions of C]*-algebras are discussed, including a result linking amalgamated products with the Busby/Hochshild theory.

Combinatorial Set Theory of C*-algebras

Author : Ilijas Farah
Publisher : Springer Nature
ISBN 13 : 3030270939
Total Pages : 535 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Combinatorial Set Theory of C*-algebras by : Ilijas Farah

Download or read book Combinatorial Set Theory of C*-algebras written by Ilijas Farah and published by Springer Nature. This book was released on 2019-12-24 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores and highlights the fertile interaction between logic and operator algebras, which in recent years has led to the resolution of several long-standing open problems on C*-algebras. The interplay between logic and operator algebras (C*-algebras, in particular) is relatively young and the author is at the forefront of this interaction. The deep level of scholarship contained in these pages is evident and opens doors to operator algebraists interested in learning about the set-theoretic methods relevant to their field, as well as to set-theorists interested in expanding their view to the non-commutative realm of operator algebras. Enough background is included from both subjects to make the book a convenient, self-contained source for students. A fair number of the exercises form an integral part of the text. They are chosen to widen and deepen the material from the corresponding chapters. Some other exercises serve as a warmup for the latter chapters.

Operator Algebra and Dynamics

Author : Toke M. Carlsen
Publisher : Springer Science & Business Media
ISBN 13 : 3642394590
Total Pages : 343 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Operator Algebra and Dynamics by : Toke M. Carlsen

Download or read book Operator Algebra and Dynamics written by Toke M. Carlsen and published by Springer Science & Business Media. This book was released on 2013-12-03 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on presentations given at the NordForsk Network Closing Conference “Operator Algebra and Dynamics,” held in Gjáargarður, Faroe Islands, in May 2012, this book features high quality research contributions and review articles by researchers associated with the NordForsk network and leading experts that explore the fundamental role of operator algebras and dynamical systems in mathematics with possible applications to physics, engineering and computer science. It covers the following topics: von Neumann algebras arising from discrete measured groupoids, purely infinite Cuntz-Krieger algebras, filtered K-theory over finite topological spaces, C*-algebras associated to shift spaces (or subshifts), graph C*-algebras, irrational extended rotation algebras that are shown to be C*-alloys, free probability, renewal systems, the Grothendieck Theorem for jointly completely bounded bilinear forms on C*-algebras, Cuntz-Li algebras associated with the a-adic numbers, crossed products of injective endomorphisms (the so-called Stacey crossed products), the interplay between dynamical systems, operator algebras and wavelets on fractals, C*-completions of the Hecke algebra of a Hecke pair, semiprojective C*-algebras, and the topological dimension of type I C*-algebras. Operator Algebra and Dynamics will serve as a useful resource for a broad spectrum of researchers and students in mathematics, physics, and engineering.

Algebraic Methods in Functional Analysis

Author : Ivan G. Todorov
Publisher : Springer Science & Business Media
ISBN 13 : 3034805020
Total Pages : 301 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Algebraic Methods in Functional Analysis by : Ivan G. Todorov

Download or read book Algebraic Methods in Functional Analysis written by Ivan G. Todorov and published by Springer Science & Business Media. This book was released on 2013-10-25 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises the proceedings of the Conference on Operator Theory and its Applications held in Gothenburg, Sweden, April 26-29, 2011. The conference was held in honour of Professor Victor Shulman on the occasion of his 65th birthday. The papers included in the volume cover a large variety of topics, among them the theory of operator ideals, linear preservers, C*-algebras, invariant subspaces, non-commutative harmonic analysis, and quantum groups, and reflect recent developments in these areas. The book consists of both original research papers and high quality survey articles, all of which were carefully refereed.

An Introduction to the Classification of Amenable C*-algebras

Author : Huaxin Lin
Publisher : World Scientific
ISBN 13 : 9789812799883
Total Pages : 336 pages
Book Rating : 4.7/5 (998 download)

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Book Synopsis An Introduction to the Classification of Amenable C*-algebras by : Huaxin Lin

Download or read book An Introduction to the Classification of Amenable C*-algebras written by Huaxin Lin and published by World Scientific. This book was released on 2001 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory and applications of C Oeu -algebras are related to fields ranging from operator theory, group representations and quantum mechanics, to non-commutative geometry and dynamical systems. By Gelfand transformation, the theory of C Oeu -algebras is also regarded as non-commutative topology. About a decade ago, George A. Elliott initiated the program of classification of C Oeu -algebras (up to isomorphism) by their K -theoretical data. It started with the classification of AT -algebras with real rank zero. Since then great efforts have been made to classify amenable C Oeu -algebras, a class of C Oeu -algebras that arises most naturally. For example, a large class of simple amenable C Oeu -algebras is discovered to be classifiable. The application of these results to dynamical systems has been established. This book introduces the recent development of the theory of the classification of amenable C Oeu -algebras OCo the first such attempt. The first three chapters present the basics of the theory of C Oeu -algebras which are particularly important to the theory of the classification of amenable C Oeu -algebras. Chapter 4 otters the classification of the so-called AT -algebras of real rank zero. The first four chapters are self-contained, and can serve as a text for a graduate course on C Oeu -algebras. The last two chapters contain more advanced material. In particular, they deal with the classification theorem for simple AH -algebras with real rank zero, the work of Elliott and Gong. The book contains many new proofs and some original results related to the classification of amenable C Oeu -algebras. Besides being as an introduction to the theory of the classification of amenable C Oeu -algebras, it is a comprehensive reference for those more familiar with the subject. Sample Chapter(s). Chapter 1.1: Banach algebras (260 KB). Chapter 1.2: C*-algebras (210 KB). Chapter 1.3: Commutative C*-algebras (212 KB). Chapter 1.4: Positive cones (207 KB). Chapter 1.5: Approximate identities, hereditary C*-subalgebras and quotients (230 KB). Chapter 1.6: Positive linear functionals and a Gelfand-Naimark theorem (235 KB). Chapter 1.7: Von Neumann algebras (234 KB). Chapter 1.8: Enveloping von Neumann algebras and the spectral theorem (217 KB). Chapter 1.9: Examples of C*-algebras (270 KB). Chapter 1.10: Inductive limits of C*-algebras (252 KB). Chapter 1.11: Exercises (220 KB). Chapter 1.12: Addenda (168 KB). Contents: The Basics of C Oeu -Algebras; Amenable C Oeu -Algebras and K -Theory; AF- Algebras and Ranks of C Oeu -Algebras; Classification of Simple AT -Algebras; C Oeu -Algebra Extensions; Classification of Simple Amenable C Oeu -Algebras. Readership: Researchers and graduate students in operator algebras."

K-Theory for Operator Algebras

Author : Bruce Blackadar
Publisher : Cambridge University Press
ISBN 13 : 9780521635325
Total Pages : 326 pages
Book Rating : 4.6/5 (353 download)

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Book Synopsis K-Theory for Operator Algebras by : Bruce Blackadar

Download or read book K-Theory for Operator Algebras written by Bruce Blackadar and published by Cambridge University Press. This book was released on 1998-09-13 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the only comprehensive treatment of K-theory for operator algebras.

Covering Dimension of C*-Algebras and 2-Coloured Classification

Author : Joan Bosa
Publisher : American Mathematical Soc.
ISBN 13 : 1470434709
Total Pages : 112 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Covering Dimension of C*-Algebras and 2-Coloured Classification by : Joan Bosa

Download or read book Covering Dimension of C*-Algebras and 2-Coloured Classification written by Joan Bosa and published by American Mathematical Soc.. This book was released on 2019-02-21 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors introduce the concept of finitely coloured equivalence for unital -homomorphisms between -algebras, for which unitary equivalence is the -coloured case. They use this notion to classify -homomorphisms from separable, unital, nuclear -algebras into ultrapowers of simple, unital, nuclear, -stable -algebras with compact extremal trace space up to -coloured equivalence by their behaviour on traces; this is based on a -coloured classification theorem for certain order zero maps, also in terms of tracial data. As an application the authors calculate the nuclear dimension of non-AF, simple, separable, unital, nuclear, -stable -algebras with compact extremal trace space: it is 1. In the case that the extremal trace space also has finite topological covering dimension, this confirms the remaining open implication of the Toms-Winter conjecture. Inspired by homotopy-rigidity theorems in geometry and topology, the authors derive a “homotopy equivalence implies isomorphism” result for large classes of -algebras with finite nuclear dimension.

Classification of Nuclear C*-Algebras. Entropy in Operator Algebras

Author : M. Rordam
Publisher : Springer Science & Business Media
ISBN 13 : 3662048256
Total Pages : 206 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Classification of Nuclear C*-Algebras. Entropy in Operator Algebras by : M. Rordam

Download or read book Classification of Nuclear C*-Algebras. Entropy in Operator Algebras written by M. Rordam and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated in a series of papers by Murray and von Neumann in the 1930's and 1940's. A von Neumann algebra is a self-adjoint unital subalgebra M of the algebra of bounded operators of a Hilbert space which is closed in the weak operator topology. According to von Neumann's bicommutant theorem, M is closed in the weak operator topology if and only if it is equal to the commutant of its commutant. Afactor is a von Neumann algebra with trivial centre and the work of Murray and von Neumann contained a reduction of all von Neumann algebras to factors and a classification of factors into types I, II and III. C* -algebras are self-adjoint operator algebras on Hilbert space which are closed in the norm topology. Their study was begun in the work of Gelfand and Naimark who showed that such algebras can be characterized abstractly as involutive Banach algebras, satisfying an algebraic relation connecting the norm and the involution. They also obtained the fundamental result that a commutative unital C* -algebra is isomorphic to the algebra of complex valued continuous functions on a compact space - its spectrum. Since then the subject of operator algebras has evolved into a huge mathematical endeavour interacting with almost every branch of mathematics and several areas of theoretical physics.

Model Theory of $mathrm {C}^*$-Algebras

$Download Model Theory of $mathrm {C}^*$-Algebras PDF Online Free$

Author : Ilijas Farah
Publisher : American Mathematical Society
ISBN 13 : 1470447576
Total Pages : 127 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Model Theory of $mathrm {C}^*$-Algebras by : Ilijas Farah

Download or read book Model Theory of $mathrm {C}^*$-Algebras written by Ilijas Farah and published by American Mathematical Society. This book was released on 2021-09-24 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

E-recursion, Forcing And C*-algebras

Author : Chi Tat Chong
Publisher : World Scientific
ISBN 13 : 9814602655
Total Pages : 228 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis E-recursion, Forcing And C*-algebras by : Chi Tat Chong

Download or read book E-recursion, Forcing And C*-algebras written by Chi Tat Chong and published by World Scientific. This book was released on 2014-05-28 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the lecture notes of short courses given by three leading experts in mathematical logic at the 2012 Asian Initiative for Infinity Logic Summer School. The major topics cover set-theoretic forcing, higher recursion theory, and applications of set theory to C*-algebra. This volume offers a wide spectrum of ideas and techniques introduced in contemporary research in the field of mathematical logic to students, researchers and mathematicians.

Operator Algebras

Author : Ola Bratteli
Publisher : Springer Science & Business Media
ISBN 13 : 3540341978
Total Pages : 280 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Operator Algebras by : Ola Bratteli

Download or read book Operator Algebras written by Ola Bratteli and published by Springer Science & Business Media. This book was released on 2007-01-19 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theme of the first Abel Symposium was operator algebras in a wide sense. In the last 40 years operator algebras have developed from a rather special discipline within functional analysis to become a central field in mathematics often described as "non-commutative geometry". It has branched out in several sub-disciplines and made contact with other subjects. The contributions to this volume give a state-of-the-art account of some of these sub-disciplines and the variety of topics reflect to some extent how the subject has developed. This is the first volume in a prestigious new book series linked to the Abel prize.

Operator Algebras

Author : Bruce Blackadar
Publisher : Springer Science & Business Media
ISBN 13 : 3540285172
Total Pages : 530 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Operator Algebras by : Bruce Blackadar

Download or read book Operator Algebras written by Bruce Blackadar and published by Springer Science & Business Media. This book was released on 2006-03-09 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive introduction to the general theory of C*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity and exactness, crossed products, K-theory, and quasidiagonality. The presentation carefully and precisely explains the main features of each part of the theory of operator algebras; most important arguments are at least outlined and many are presented in full detail.

Model Theory of Operator Algebras

Author : Isaac Goldbring
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110768283
Total Pages : 498 pages
Book Rating : 4.1/5 (17 download)

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Book Synopsis Model Theory of Operator Algebras by : Isaac Goldbring

Download or read book Model Theory of Operator Algebras written by Isaac Goldbring and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-07-24 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuous model theory is an extension of classical first order logic which is best suited for classes of structures which are endowed with a metric. Applications have grown considerably in the past decade. This book is dedicated to showing how the techniques of continuous model theory are used to study C*-algebras and von Neumann algebras. This book geared to researchers in both logic and functional analysis provides the first self-contained collection of articles surveying the many applications of continuous logic to operator algebras that have been obtained in the last 15 years.

Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture

Author : Valerio Capraro
Publisher : Springer
ISBN 13 : 3319193333
Total Pages : 157 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture by : Valerio Capraro

Download or read book Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture written by Valerio Capraro and published by Springer. This book was released on 2015-10-12 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of many results, are presented in the framework of model theory for metric structures. This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems. Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices. These deep and fruitful notions, introduced by Gromov and Radulescu, respectively, in the late 1990s, stimulated an impressive amount of research in the last 15 years, touching several seemingly distant areas of mathematics including geometric group theory, operator algebras, dynamical systems, graph theory, and quantum information theory. Several long-standing conjectures, still open for arbitrary groups, are now settled for sofic or hyperlinear groups. The presentation is self-contained and accessible to anyone with a graduate-level mathematical background. In particular, no specific knowledge of logic or model theory is required. The monograph also contains many exercises, to help familiarize the reader with the topics present.

Coxeter Groups and Hopf Algebras

Author : Marcelo Aguiar
Publisher : American Mathematical Soc.
ISBN 13 : 0821853546
Total Pages : 201 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Coxeter Groups and Hopf Algebras by : Marcelo Aguiar

Download or read book Coxeter Groups and Hopf Algebras written by Marcelo Aguiar and published by American Mathematical Soc.. This book was released on 2006 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: An important idea in the work of G.-C. Rota is that certain combinatorial objects give rise to Hopf algebras that reflect the manner in which these objects compose and decompose. Recent work has seen the emergence of several interesting Hopf algebras of this kind, which connect diverse subjects such as combinatorics, algebra, geometry, and theoretical physics. This monograph presents a novel geometric approach using Coxeter complexes and the projection maps of Tits for constructing and studying many of these objects as well as new ones. The first three chapters introduce the necessary background ideas making this work accessible to advanced graduate students. The later chapters culminate in a unified and conceptual construction of several Hopf algebras based on combinatorial objects which emerge naturally from the geometric viewpoint. This work lays a foundation and provides new insights for further development of the subject.

Quanta of Maths

Author : Institut des hautes études scientifiques (Paris, France)
Publisher : American Mathematical Soc.
ISBN 13 : 0821852035
Total Pages : 695 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Quanta of Maths by : Institut des hautes études scientifiques (Paris, France)

Download or read book Quanta of Maths written by Institut des hautes études scientifiques (Paris, France) and published by American Mathematical Soc.. This book was released on 2010 with total page 695 pages. Available in PDF, EPUB and Kindle. Book excerpt: The work of Alain Connes has cut a wide swath across several areas of mathematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics. Specific themes covered by the articles are as follows: entropy in operator algebras, regular $C^*$-algebras of integral domains, properly infinite $C^*$-algebras, representations of free groups and 1-cohomology, Leibniz seminorms and quantum metric spaces; von Neumann algebras, fundamental Group of $\mathrm{II}_1$ factors, subfactors and planar algebras; Baum-Connes conjecture and property T, equivariant K-homology, Hermitian K-theory; cyclic cohomology, local index formula and twisted spectral triples, tangent groupoid and the index theorem; noncommutative geometry and space-time, spectral action principle, quantum gravity, noncommutative ADHM and instantons, non-compact spectral triples of finite volume, noncommutative coordinate algebras; Hopf algebras, Vinberg algebras, renormalization and combinatorics, motivic renormalization and singularities; cyclotomy and analytic geometry over $F_1$, quantum modular forms; differential K-theory, cyclic theory and S-cohomology.