Lifting Solutions To Perturbing Problems In C Algebras
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Lifting Solutions To Perturbing Problems In C Algebras
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Author : Terry A. Loring
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-01-01
Lifting Solutions To Perturbing Problems In C Algebras written by Terry A. Loring 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 1997-01-01 with Mathematics categories.
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
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Author : Ilijas Farah
language : en
Publisher: Springer Nature
Release Date : 2019-12-24
Combinatorial Set Theory Of C Algebras written by Ilijas Farah and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-24 with Mathematics categories.
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.
Covering Dimension Of C Algebras And 2 Coloured Classification
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Author : Joan Bosa
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-02-21
Covering Dimension Of C Algebras And 2 Coloured Classification written by Joan Bosa 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 2019-02-21 with C*-algebras categories.
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.
Tensor Products Of C Algebras And Operator Spaces
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Author : Gilles Pisier
language : en
Publisher: Cambridge University Press
Release Date : 2020-02-27
Tensor Products Of C Algebras And Operator Spaces written by Gilles Pisier 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 2020-02-27 with Mathematics categories.
Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.
Model Theory Of Mathrm C Algebras
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Author : Ilijas Farah
language : en
Publisher: American Mathematical Society
Release Date : 2021-09-24
Model Theory Of Mathrm C Algebras written by Ilijas Farah and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-24 with Mathematics categories.
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E Recursion Forcing And C Algebras
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Author : Chi Tat Chong
language : en
Publisher: World Scientific
Release Date : 2014-05-28
E Recursion Forcing And C Algebras written by Chi Tat Chong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-28 with Mathematics categories.
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
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Author : Ola Bratteli
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-19
Operator Algebras written by Ola Bratteli 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 2007-01-19 with Mathematics categories.
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
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Author : Bruce Blackadar
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-09
Operator Algebras written by Bruce Blackadar 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 2006-03-09 with Mathematics categories.
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.
Algebraic Methods In Functional Analysis
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Author : Ivan G. Todorov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-25
Algebraic Methods In Functional Analysis written by Ivan G. Todorov 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 2013-10-25 with Mathematics categories.
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.
Model Theory Of Operator Algebras
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Author : Isaac Goldbring
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-07-24
Model Theory Of Operator Algebras written by Isaac Goldbring and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-24 with Mathematics categories.
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.