[PDF] Full Groups With The Haagerup Property Which Are Not Weakly Amenable Download eBook

Operator Algebras and Applications

Author: Toke M. Carlsen

Publisher: Springer

Published: 2016-07-30

Total Pages: 350

ISBN-13: 3319392867

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.

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

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

Author: Nathanial Patrick Brown

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 530

ISBN-13: 0821843818

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$\textrm{C}*$-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.

Groups with the Haagerup Property

Author: Pierre-Alain Cherix

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 130

ISBN-13: 3034882378

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A locally compact group has the Haagerup property, or is a-T-menable in the sense of Gromov, if it admits a proper isometric action on some affine Hilbert space. As Gromov's pun is trying to indicate, this definition is designed as a strong negation to Kazhdan's property (T), characterized by the fact that every isometric action on some affine Hilbert space has a fixed point. This book is to covers various aspects of the Haagerup property. It gives several new examples.

Tensor Products of C*-algebras and Operator Spaces

Author: Gilles Pisier

Publisher: Cambridge University Press

Published: 2020-02-27

Total Pages: 495

ISBN-13: 1108479014

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Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.

Linear and Complex Analysis Problem Book 3

Author: Victor P. Havin

Publisher: Springer

Published: 2006-12-08

Total Pages: 517

ISBN-13: 3540483675

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The 2-volume book is an updated, reorganized and considerably enlarged version of the previous edition of the Research Problem Book in Analysis (LNM 1043), a collection familiar to many analysts, that has sparked off much research. This new edition, created in a joint effort by a large team of analysts, is, like its predecessor, a collection of unsolved problems of modern analysis designed as informally written mini-articles, each containing not only a statement of a problem but also historical and methodological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references. There are now 342 of these mini- articles, almost twice as many as in the previous edition, despite the fact that a good deal of them have been solved!

Asymptotic Combinatorics with Applications to Mathematical Physics

Author: Anatoly M. Vershik

Publisher: Springer

Published: 2003-07-03

Total Pages: 245

ISBN-13: 354044890X

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At the Summer School Saint Petersburg 2001, the main lecture courses bore on recent progress in asymptotic representation theory: those written up for this volume deal with the theory of representations of infinite symmetric groups, and groups of infinite matrices over finite fields; Riemann-Hilbert problem techniques applied to the study of spectra of random matrices and asymptotics of Young diagrams with Plancherel measure; the corresponding central limit theorems; the combinatorics of modular curves and random trees with application to QFT; free probability and random matrices, and Hecke algebras.