Type Iii Factors And Index Theory

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Theory of Operator Algebras III

Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
ISBN 13 : 9783540429135
Total Pages : 580 pages
Book Rating : 4.4/5 (291 download)

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Book Synopsis Theory of Operator Algebras III by : Masamichi Takesaki

Download or read book Theory of Operator Algebras III written by Masamichi Takesaki and published by Springer Science & Business Media. This book was released on 2002-11-01 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "These three bulky volumes [EMS 124, 125, 127] [...] provide an introduction to this rapidly developing theory. [...] These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of mathematics. Furthermore, they should be on the bookshelf of every researcher of the area." Acta Scientiarum Mathematicarum

Higher Index Theory

Author : Rufus Willett
Publisher : Cambridge University Press
ISBN 13 : 1108853110
Total Pages : 595 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Higher Index Theory by : Rufus Willett

Download or read book Higher Index Theory written by Rufus Willett and published by Cambridge University Press. This book was released on 2020-07-02 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from the K-theory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, large-scale geometry, manifold topology and geometry, and operator algebras. Aimed at geometers, topologists and operator algebraists, this book takes a friendly and concrete approach to this exciting theory, focusing on the main conjectures in the area and their applications outside of it. A well-balanced combination of detailed introductory material (with exercises), cutting-edge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike.

Noncommutative Geometry

Author : Alain Connes
Publisher : Springer
ISBN 13 : 3540397027
Total Pages : 364 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Noncommutative Geometry by : Alain Connes

Download or read book Noncommutative Geometry written by Alain Connes and published by Springer. This book was released on 2003-12-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

Modular Theory in Operator Algebras

Author : Şerban Strǎtilǎ
Publisher : Cambridge University Press
ISBN 13 : 1108489605
Total Pages : 461 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Modular Theory in Operator Algebras by : Şerban Strǎtilǎ

Download or read book Modular Theory in Operator Algebras written by Şerban Strǎtilǎ and published by Cambridge University Press. This book was released on 2020-12-03 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses the fundamentals and latest developments in operator algebras, focusing on continuous and discrete decomposition of factors of type III.

Mathematical Problems in Quantum Physics

Author : Federico Bonetto
Publisher : American Mathematical Soc.
ISBN 13 : 1470436817
Total Pages : 346 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Mathematical Problems in Quantum Physics by : Federico Bonetto

Download or read book Mathematical Problems in Quantum Physics written by Federico Bonetto and published by American Mathematical Soc.. This book was released on 2018-10-24 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the QMATH13: Mathematical Results in Quantum Physics conference, held from October 8–11, 2016, at the Georgia Institute of Technology, Atlanta, Georgia. In recent years, a number of new frontiers have opened in mathematical physics, such as many-body localization and Schrödinger operators on graphs. There has been progress in developing mathematical techniques as well, notably in renormalization group methods and the use of Lieb–Robinson bounds in various quantum models. The aim of this volume is to provide an overview of some of these developments. Topics include random Schrödinger operators, many-body fermionic systems, atomic systems, effective equations, and applications to quantum field theory. A number of articles are devoted to the very active area of Schrödinger operators on graphs and general spectral theory of Schrödinger operators. Some of the articles are expository and can be read by an advanced graduate student.

Index Theory and Operator Algebras

Author : Jeffrey Stephen Fox
Publisher : American Mathematical Soc.
ISBN 13 : 0821851527
Total Pages : 202 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Index Theory and Operator Algebras by : Jeffrey Stephen Fox

Download or read book Index Theory and Operator Algebras written by Jeffrey Stephen Fox and published by American Mathematical Soc.. This book was released on 1993 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of papers by leading researchers provides a broad picture of current research directions in index theory. Based on lectures presented at the NSF-CBMS Regional Conference on $K$-Homology and Index Theory, held in August, 1991 at the University of Colorado at Boulder, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Presented here are two new proofs of the classical Atiyah-Singer Index Theorem, as well as index theorems for manifolds with boundary and open manifolds. Index theory for semi-simple $p$-adic groups and the geometry of discrete groups are also discussed. Throughout the book, the application of operator algebras emerges as a central theme. Aimed at graduate students and researchers, this book is suitable as a text for an advanced graduate course on index theory.

Theory of Operator Algebras II

Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
ISBN 13 : 9783540429142
Total Pages : 552 pages
Book Rating : 4.4/5 (291 download)

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Book Synopsis Theory of Operator Algebras II by : Masamichi Takesaki

Download or read book Theory of Operator Algebras II written by Masamichi Takesaki and published by Springer Science & Business Media. This book was released on 2002-11-01 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Together with Theory of Operator Algebras I and III, this book presents the theory of von Neumann algebras and non-commutative integration focusing on the group of automorphisms and the structure analysis. From the reviews: "These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of mathematics. Furthermore, they should be on the bookshelf of every researcher of the area." --ACTA SCIENTIARUM MATHEMATICARUM

Index Theory in von Neumann Algebras

Author : Catherine Louise Olsen
Publisher : American Mathematical Soc.
ISBN 13 : 0821822950
Total Pages : 78 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Index Theory in von Neumann Algebras by : Catherine Louise Olsen

Download or read book Index Theory in von Neumann Algebras written by Catherine Louise Olsen and published by American Mathematical Soc.. This book was released on 1984 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of this paper is to define a natural analytic index function on an arbitrary von Neumann algebra relative to an arbitrary ideal. This index map enables us to develop a complete Fredholm and semi-Fredholm theory in this setting which is parallel to classical Fredholm and semi-Fredholm theory.

Von Neumann Algebras

Author : J. Dixmier
Publisher : Elsevier
ISBN 13 : 0080960154
Total Pages : 479 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Von Neumann Algebras by : J. Dixmier

Download or read book Von Neumann Algebras written by J. Dixmier and published by Elsevier. This book was released on 2011-08-18 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study, under the name of von Neumann algebras, those algebras generally known as “rings of operators“ or “W*-algebras.“ The new terminology, suggested by J. Dieudonng, is fully justified from the historical point of view. Certain of the results are valid for more general algebras. We have, however systematically avoided this kind of generalization, except when it would facilitate the study of von Neumann algebras themselves. Parts I and I1 comprise those results which at present appear to’be the most useful for applications, although we do not embark on the study of those applications. Part 111, which is more technical, is primarily intended for specialists; it is virtually independent of Part 11.

Invariance Theory

Author : Peter B. Gilkey
Publisher : CRC Press
ISBN 13 : 9780849378744
Total Pages : 534 pages
Book Rating : 4.3/5 (787 download)

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Book Synopsis Invariance Theory by : Peter B. Gilkey

Download or read book Invariance Theory written by Peter B. Gilkey and published by CRC Press. This book was released on 1994-12-22 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.

Category Theory in Context

Author : Emily Riehl
Publisher : Courier Dover Publications
ISBN 13 : 0486820807
Total Pages : 273 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Category Theory in Context by : Emily Riehl

Download or read book Category Theory in Context written by Emily Riehl and published by Courier Dover Publications. This book was released on 2017-03-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.

Lectures on Operator Theory

Author : B. V. Rajarama Bhat
Publisher : American Mathematical Soc.
ISBN 13 : 0821808214
Total Pages : 337 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lectures on Operator Theory by : B. V. Rajarama Bhat

Download or read book Lectures on Operator Theory written by B. V. Rajarama Bhat and published by American Mathematical Soc.. This book was released on 1999 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book resulted from the lectures held at The Fields Institute (Waterloo, ON, Canada). Leading international experts presented current results on the theory of C*-algebras and von Neumann algebras, together with recent work on the classification of C*-algebras. Much of the material in the book is appearing here for the first time and is not available elsewhere in the literature.

Categories for the Working Mathematician

Author : Saunders Mac Lane
Publisher : Springer Science & Business Media
ISBN 13 : 1475747217
Total Pages : 320 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Categories for the Working Mathematician by : Saunders Mac Lane

Download or read book Categories for the Working Mathematician written by Saunders Mac Lane and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.

Spectral Theory and Quantum Mechanics

Author : Valter Moretti
Publisher : Springer
ISBN 13 : 331970706X
Total Pages : 962 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Spectral Theory and Quantum Mechanics by : Valter Moretti

Download or read book Spectral Theory and Quantum Mechanics written by Valter Moretti and published by Springer. This book was released on 2018-01-30 with total page 962 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory. Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories. Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing and presenting the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly."

Recent Advances in Operator Theory, Operator Algebras, and their Applications

Author : Dumitru Gaspar
Publisher : Springer Science & Business Media
ISBN 13 : 3764373148
Total Pages : 351 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Recent Advances in Operator Theory, Operator Algebras, and their Applications by : Dumitru Gaspar

Download or read book Recent Advances in Operator Theory, Operator Algebras, and their Applications written by Dumitru Gaspar and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers peer-reviewed articles from the 19th International Conference on Operator Theory, Summer 2002. It contains recent developments in a broad range of topics from operator theory, operator algebras and their applications, particularly to differential analysis, complex functions, ergodic theory, mathematical physics, matrix analysis, and systems theory. The book covers a large variety of topics including single operator theory, C*-algebras, diffrential operators, integral transforms, stochastic processes and operators, and more.

Quantum Theory

Author : Peter Bongaarts
Publisher : Springer
ISBN 13 : 3319095617
Total Pages : 460 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Quantum Theory by : Peter Bongaarts

Download or read book Quantum Theory written by Peter Bongaarts and published by Springer. This book was released on 2014-12-01 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures – a fact not usually emphasized in standard physics textbooks – which makes it easy for mathematicians to understand their basic features. It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.

Ergodic Theory

Author : Cesar E. Silva
Publisher : Springer Nature
ISBN 13 : 1071623885
Total Pages : 707 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Ergodic Theory by : Cesar E. Silva

Download or read book Ergodic Theory written by Cesar E. Silva and published by Springer Nature. This book was released on 2023-07-31 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras