Classification Of Nuclear C Algebras Entropy In Operator Algebras

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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.

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

Author : Mikael Rørdam
Publisher :
ISBN 13 :
Total Pages : 198 pages
Book Rating : 4.:/5 (472 download)

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Book Synopsis Classification of Nuclear C*-algebras. Entropy in Operator Algebras by : Mikael Rørdam

Download or read book Classification of Nuclear C*-algebras. Entropy in Operator Algebras written by Mikael Rørdam and published by . This book was released on 2002 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

Author : Mikael Rørdam
Publisher :
ISBN 13 :
Total Pages : 198 pages
Book Rating : 4.:/5 (87 download)

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Book Synopsis Classification of Nuclear C*-algebras. Entropy in Operator Algebras by : Mikael Rørdam

Theory of Operator Algebras I

Author : M. Takesaki
Publisher : Springer
ISBN 13 : 9783540422488
Total Pages : 415 pages
Book Rating : 4.4/5 (224 download)

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Book Synopsis Theory of Operator Algebras I by : M. Takesaki

Download or read book Theory of Operator Algebras I written by M. Takesaki and published by Springer. This book was released on 2001-11-20 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three-volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects.

Dynamical Entropy in Operator Algebras

Author : Sergey Neshveyev
Publisher : Springer Science & Business Media
ISBN 13 : 3540346732
Total Pages : 294 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Dynamical Entropy in Operator Algebras by : Sergey Neshveyev

Download or read book Dynamical Entropy in Operator Algebras written by Sergey Neshveyev and published by Springer Science & Business Media. This book was released on 2006-09-22 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book addresses mathematicians and physicists, including graduate students, who are interested in quantum dynamical systems and applications of operator algebras and ergodic theory. It is the only monograph on this topic. Although the authors assume a basic knowledge of operator algebras, they give precise definitions of the notions and in most cases complete proofs of the results which are used.

Operator Algebras

Author : Bruce Blackadar
Publisher : Springer Science & Business Media
ISBN 13 : 3540285172
Total Pages : 528 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 528 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.

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

Author : Joan Bosa
Publisher : American Mathematical Soc.
ISBN 13 : 1470434709
Total Pages : 97 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 97 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.

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.

$\textrm {C}^*$-Algebras and Finite-Dimensional Approximations

$Download $\textrm {C}^*$-Algebras and Finite-Dimensional Approximations PDF Online Free$

Author : Nathanial Patrick Brown
Publisher : American Mathematical Soc.
ISBN 13 : 0821843818
Total Pages : 530 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis $\textrm {C}^*$-Algebras and Finite-Dimensional Approximations by : Nathanial Patrick Brown

Download or read book $\textrm {C}^*$-Algebras and Finite-Dimensional Approximations written by Nathanial Patrick Brown and published by American Mathematical Soc.. This book was released on 2008 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: $\textrm{C}*$-approximation theory has provided the foundation for many of the most important conceptual breakthroughs and applications of operator algebras. This book systematically studies (most of) the numerous types of approximation properties that have been important in recent years: nuclearity, exactness, quasidiagonality, local reflexivity, and others. Moreover, it contains user-friendly proofs, insofar as that is possible, of many fundamental results that were previously quite hard to extract from the literature. Indeed, perhaps the most important novelty of the first ten chapters is an earnest attempt to explain some fundamental, but difficult and technical, results as painlessly as possible. The latter half of the book presents related topics and applications--written with researchers and advanced, well-trained students in mind. The authors have tried to meet the needs both of students wishing to learn the basics of an important area of research as well as researchers who desire a fairly comprehensive reference for the theory and applications of $\textrm{C}*$-approximation theory.

Crossed Products of C*-algebras

Author : Dana P. Williams
Publisher : American Mathematical Soc.
ISBN 13 : 0821842420
Total Pages : 528 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Crossed Products of C*-algebras by : Dana P. Williams

Download or read book Crossed Products of C*-algebras written by Dana P. Williams and published by American Mathematical Soc.. This book was released on 2007 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of crossed products is extremely rich and intriguing. There are applications not only to operator algebras, but to subjects as varied as noncommutative geometry and mathematical physics. This book provides a detailed introduction to this vast subject suitable for graduate students and others whose research has contact with crossed product $C*$-algebras. In addition to providing the basic definitions and results, the main focus of this book is the fine ideal structure of crossed products as revealed by the study of induced representations via the Green-Mackey-Rieffel machine. In particular, there is an in-depth analysis of the imprimitivity theorems on which Rieffel's theory of induced representations and Morita equivalence of $C*$-algebras are based. There is also a detailed treatment of the generalized Effros-Hahn conjecture and its proof due to Gootman, Rosenberg, and Sauvageot. This book is meant to be self-contained and accessible to any graduate student coming out of a first course on operator algebras. There are appendices that deal with ancillary subjects, which while not central to the subject, are nevertheless crucial for a complete understanding of the material. Some of the appendices will be of independent interest. To view another book by this author, please visit Morita Equivalence and Continuous-Trace $C*$-Algebras.

Mexican Mathematicians in the World

Author : Fernando Galaz-García
Publisher : American Mathematical Society
ISBN 13 : 1470465361
Total Pages : 319 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Mexican Mathematicians in the World by : Fernando Galaz-García

Download or read book Mexican Mathematicians in the World written by Fernando Galaz-García and published by American Mathematical Society. This book was released on 2021-11-22 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles in this volume are based on presentations given at the IV Meeting of Mexican Mathematicians Abroad (IV Reunión de Matemáticos Mexicanos en el Mundo), held from June 10–15, 2018, at Casa Matemática Oaxaca (CMO), Mexico. This meeting was the fourth in a series of ongoing biannual meetings bringing together Mexican mathematicians working abroad with their peers in Mexico. This book features surveys and research articles from five broad research areas: algebra, analysis, combinatorics, geometry, and topology. Their topics range from general relativity and mathematical physics to interactions between logic and ergodic theory. Several articles provide a panoramic view of the fields and problems on which the authors are currently working on, showcasing diverse research lines complementary to those currently pursued in Mexico. The research-oriented manuscripts provide either alternative approaches to well-known problems or new advances in active research fields.

Integral Representation Theory

Author : Jaroslav Lukeš
Publisher : Walter de Gruyter
ISBN 13 : 3110203219
Total Pages : 732 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Integral Representation Theory by : Jaroslav Lukeš

Download or read book Integral Representation Theory written by Jaroslav Lukeš and published by Walter de Gruyter. This book was released on 2009-12-22 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet’s theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book form for the first time. The text is self-contained and covers a wide range of applications. From the contents: Geometry of convex sets Choquet theory of function spaces Affine functions on compact convex sets Perfect classes of functions and representation of affine functions Simplicial function spaces Choquet's theory of function cones Topologies on boundaries Several results on function spaces and compact convex sets Continuous and measurable selectors Construction of function spaces Function spaces in potential theory and Dirichlet problem Applications

Operator Algebras and Applications

Author : Toke M. Carlsen
Publisher : Springer
ISBN 13 : 3319392867
Total Pages : 348 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Operator Algebras and Applications by : Toke M. Carlsen

Download or read book Operator Algebras and Applications written by Toke M. Carlsen and published by Springer. This book was released on 2016-07-30 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on operator algebras. It is interesting to see the remarkable advances that have been made in operator algebras over these years, which strikingly illustrate the vitality of the field. A total of 26 talks were given at the symposium on a variety of themes, all highlighting the richness of the subject. The field of operator algebras was created in the 1930s and was motivated by problems of quantum mechanics. It has subsequently developed well beyond its initial intended realm of applications and expanded into such diverse areas of mathematics as representation theory, dynamical systems, differential geometry, number theory and quantum algebra. One branch, known as “noncommutative geometry”, has become a powerful tool for studying phenomena that are beyond the reach of classical analysis. This volume includes research papers that present new results, surveys that discuss the development of a specific line of research, and articles that offer a combination of survey and research. These contributions provide a multifaceted portrait of beautiful mathematics that both newcomers to the field of operator algebras and seasoned researchers alike will appreciate.

The Mapping Class Group from the Viewpoint of Measure Equivalence Theory

Author : Yoshikata Kida
Publisher : American Mathematical Soc.
ISBN 13 : 0821841963
Total Pages : 206 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Mapping Class Group from the Viewpoint of Measure Equivalence Theory by : Yoshikata Kida

Download or read book The Mapping Class Group from the Viewpoint of Measure Equivalence Theory written by Yoshikata Kida and published by American Mathematical Soc.. This book was released on 2008 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author obtains some classification result for the mapping class groups of compact orientable surfaces in terms of measure equivalence. In particular, the mapping class groups of different closed surfaces cannot be measure equivalent. Moreover, the author gives various examples of discrete groups which are not measure equivalent to the mapping class groups. In the course of the proof, the author investigates amenability in a measurable sense for the actions of the mapping class group on the boundary at infinity of the curve complex and on the Thurston boundary and, using this investigation, proves that the mapping class group of a compact orientable surface is exact.

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.

Crossed Products of C*-Algebras, Topological Dynamics, and Classification

Author : Thierry Giordano
Publisher : Springer
ISBN 13 : 3319708694
Total Pages : 498 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Crossed Products of C*-Algebras, Topological Dynamics, and Classification by : Thierry Giordano

Download or read book Crossed Products of C*-Algebras, Topological Dynamics, and Classification written by Thierry Giordano and published by Springer. This book was released on 2018-08-28 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the notes of the lectures given at an Advanced Course on Dynamical Systems at the Centre de Recerca Matemàtica (CRM) in Barcelona. The notes consist of four series of lectures. The first one, given by Andrew Toms, presents the basic properties of the Cuntz semigroup and its role in the classification program of simple, nuclear, separable C*-algebras. The second series of lectures, delivered by N. Christopher Phillips, serves as an introduction to group actions on C*-algebras and their crossed products, with emphasis on the simple case and when the crossed products are classifiable. The third one, given by David Kerr, treats various developments related to measure-theoretic and topological aspects of crossed products, focusing on internal and external approximation concepts, both for groups and C*-algebras. Finally, the last series of lectures, delivered by Thierry Giordano, is devoted to the theory of topological orbit equivalence, with particular attention to the classification of minimal actions by finitely generated abelian groups on the Cantor set.

Operator Algebras

Author : Ola Bratteli
Publisher : Springer Science & Business Media
ISBN 13 : 3540341978
Total Pages : 279 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 279 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.