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.

Lifting Solutions To Perturbing Problems In C Algebras

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Author : Terry A. Loring
language : en
Publisher:
Release Date : 1997

Lifting Solutions To Perturbing Problems In C Algebras written by Terry A. Loring and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with C*-algebras categories.

The nature of C^*-algebras is such that one cannot study perturbation without also studying the theory of lifting and the theory of extensions. 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 transitivity 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 techn.

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.

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.

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. ​

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 Mathematics 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.

Classification Of Nuclear C Algebras Entropy In Operator Algebras

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Author : M. Rordam
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18

Classification Of Nuclear C Algebras Entropy In Operator Algebras written by M. Rordam 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 2013-04-18 with Mathematics categories.

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.

An Introduction To The Classification Of Amenable C Algebras

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Author : Huaxin Lin
language : en
Publisher: World Scientific
Release Date : 2001-11-12

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 2001-11-12 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.

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.

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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