An Introduction To For C Algebras
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An Introduction To The Classification Of Amenable C Algebras
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Author : Huaxin Lin
language : en
Publisher: World Scientific
Release Date : 2001
An Introduction To The Classification Of Amenable C Algebras written by Huaxin Lin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The theory and applications of C?-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?-algebras is also regarded as non-commutative topology. About a decade ago, George A. Elliott initiated the program of classification of C?-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?-algebras, a class of C?-algebras that arises most naturally. For example, a large class of simple amenable C?-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?-algebras ? the first such attempt. The first three chapters present the basics of the theory of C?-algebras which are particularly important to the theory of the classification of amenable C?-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?-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?-algebras. Besides being as an introduction to the theory of the classification of amenable C?-algebras, it is a comprehensive reference for those more familiar with the subject.
An Introduction To C Algebras And The Classification Program
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Author : Karen R. Strung
language : en
Publisher: Springer Nature
Release Date : 2020-12-15
An Introduction To C Algebras And The Classification Program written by Karen R. Strung and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-15 with Mathematics categories.
This book is directed towards graduate students that wish to start from the basic theory of C*-algebras and advance to an overview of some of the most spectacular results concerning the structure of nuclear C*-algebras. The text is divided into three parts. First, elementary notions, classical theorems and constructions are developed. Then, essential examples in the theory, such as crossed products and the class of quasidiagonal C*-algebras, are examined, and finally, the Elliott invariant, the Cuntz semigroup, and the Jiang-Su algebra are defined. It is shown how these objects have played a fundamental role in understanding the fine structure of nuclear C*-algebras. To help understanding the theory, plenty of examples, treated in detail, are included. This volume will also be valuable to researchers in the area as a reference guide. It contains an extensive reference list to guide readers that wish to travel further.
An Introduction To K Theory For C Algebras
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Author : M. Rørdam
language : en
Publisher: Cambridge University Press
Release Date : 2000-07-20
An Introduction To K Theory For C Algebras written by M. Rørdam and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-20 with Mathematics categories.
This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.
An Introduction To C Algebras And Noncommutative Geometry
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Author : Heath Emerson
language : en
Publisher: Springer Nature
Release Date : 2024-07-27
An Introduction To C Algebras And Noncommutative Geometry written by Heath Emerson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-27 with Mathematics categories.
This is the first textbook on C*-algebra theory with a view toward Noncommutative Geometry. Moreover, it fills a gap in the literature, providing a clear and accessible account of the geometric picture of K-theory and its relation to the C*-algebraic picture. The text can be used as the basis for a graduate level or a capstone course with the goal being to bring a relative novice up to speed on the basic ideas while offering a glimpse at some of the more advanced topics of the subject. Coverage includes C*-algebra theory, K-theory, K-homology, Index theory and Connes’ Noncommuntative Riemannian geometry. Aimed at graduate level students, the book is also a valuable resource for mathematicians who wish to deepen their understanding of noncommutative geometry and algebraic K-theory. A wide range of important examples are introduced at the beginning of the book. There are lots of excellent exercises and any student working through these will benefit significantly. Prerequisites include a basic knowledge of algebra, analysis, and a bit of functional analysis. As the book progresses, a little more mathematical maturity is required as the text discusses smooth manifolds, some differential geometry and elliptic operator theory, and K-theory. The text is largely self-contained though occasionally the reader may opt to consult more specialized material to further deepen their understanding of certain details.
An Invitation To C Algebras
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Author : W. Arveson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Invitation To C Algebras written by W. Arveson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book gives an introduction to C*-algebras and their representations on Hilbert spaces. We have tried to present only what we believe are the most basic ideas, as simply and concretely as we could. So whenever it is convenient (and it usually is), Hilbert spaces become separable and C*-algebras become GCR. This practice probably creates an impression that nothing of value is known about other C*-algebras. Of course that is not true. But insofar as representations are con cerned, we can point to the empirical fact that to this day no one has given a concrete parametric description of even the irreducible representations of any C*-algebra which is not GCR. Indeed, there is metamathematical evidence which strongly suggests that no one ever will (see the discussion at the end of Section 3. 4). Occasionally, when the idea behind the proof of a general theorem is exposed very clearly in a special case, we prove only the special case and relegate generalizations to the exercises. In effect, we have systematically eschewed the Bourbaki tradition. We have also tried to take into account the interests of a variety of readers. For example, the multiplicity theory for normal operators is contained in Sections 2. 1 and 2. 2. (it would be desirable but not necessary to include Section 1. 1 as well), whereas someone interested in Borel structures could read Chapter 3 separately. Chapter I could be used as a bare-bones introduction to C*-algebras. Sections 2.
Stability Of Functional Equations In Banach Algebras
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Author : Yeol Je Cho
language : en
Publisher: Springer
Release Date : 2015-06-26
Stability Of Functional Equations In Banach Algebras written by Yeol Je Cho and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-26 with Mathematics categories.
Some of the most recent and significant results on homomorphisms and derivations in Banach algebras, quasi-Banach algebras, C*-algebras, C*-ternary algebras, non-Archimedean Banach algebras and multi-normed algebras are presented in this book. A brief introduction for functional equations and their stability is provided with historical remarks. Since the homomorphisms and derivations in Banach algebras are additive and R-linear or C-linear, the stability problems for additive functional equations and additive mappings are studied in detail. The latest results are discussed and examined in stability theory for new functional equations and functional inequalities in Banach algebras and C*-algebras, non-Archimedean Banach algebras, non-Archimedean C*-algebras, multi-Banach algebras and multi-C*-algebras. Graduate students with an understanding of operator theory, functional analysis, functional equations and analytic inequalities will find this book useful for furthering their understanding and discovering the latest results in mathematical analysis. Moreover, research mathematicians, physicists and engineers will benefit from the variety of old and new results, as well as theories and methods presented in this book.
Topology C Algebras And String Duality
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Author : Jonathan R_osenberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-10-27
Topology C Algebras And String Duality written by Jonathan R_osenberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-27 with Mathematics categories.
String theory is the leading candidate for a physical theory that combines all the fundamental forces of nature, as well as the principles of relativity and quantum mechanics, into a mathematically elegant whole. The mathematical tools used by string theorists are highly sophisticated, and cover many areas of mathematics. As with the birth of quantum theory in the early 20th century, the mathematics has benefited at least as much as the physics from the collaboration. In this book, based on CBMS lectures given at Texas Christian University, Rosenberg describes some of the most recent interplay between string dualities and topology and operator algebras. The book is an interdisciplinary approach to duality symmetries in string theory. It can be read by either mathematicians or theoretical physicists, and involves a more-or-less equal mixture of algebraic topology, operator algebras, and physics. There is also a bit of algebraic geometry, especially in the last chapter. The reader is assumed to be somewhat familiar with at least one of these four subjects, but not necessarily with all or even most of them. The main objective of the book is to show how several seemingly disparate subjects are closely linked with one another, and to give readers an overview of some areas of current research, even if this means that not everything is covered systematically.
Crossed Products Of C Algebras Topological Dynamics And Classification
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Author : Thierry Giordano
language : en
Publisher: Springer
Release Date : 2018-08-28
Crossed Products Of C Algebras Topological Dynamics And Classification written by Thierry Giordano and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-28 with Mathematics categories.
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 attentionto the classification of minimal actions by finitely generated abelian groups on the Cantor set.
From Sets And Types To Topology And Analysis
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Author : Laura Crosilla
language : en
Publisher: Clarendon Press
Release Date : 2005-10-06
From Sets And Types To Topology And Analysis written by Laura Crosilla and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-06 with Mathematics categories.
This edited collection bridges the foundations and practice of constructive mathematics and focusses on the contrast between the theoretical developments, which have been most useful for computer science (eg constructive set and type theories), and more specific efforts on constructive analysis, algebra and topology. Aimed at academic logicians, mathematicians, philosophers and computer scientists Including, with contributions from leading researchers, it is up-to-date, highly topical and broad in scope. This is the latest volume in the Oxford Logic Guides, which also includes: 41. J.M. Dunn and G. Hardegree: Algebraic Methods in Philosophical Logic 42. H. Rott: Change, Choice and Inference: A study of belief revision and nonmonotoic reasoning 43. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 1 44. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 2 45. David J. Pym and Eike Ritter: Reductive Logic and Proof Search: Proof theory, semantics and control 46. D.M. Gabbay and L. Maksimova: Interpolation and Definability: Modal and Intuitionistic Logics 47. John L. Bell: Set Theory: Boolean-valued models and independence proofs, third edition
Operator Algebra And Dynamics
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Author : Toke M. Carlsen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-03
Operator Algebra And Dynamics written by Toke M. Carlsen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-03 with Mathematics categories.
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.