Crossed Products Of C Algebras Topological Dynamics And Classification

Author : Thierry Giordano
Publisher : Springer
ISBN 13 : 3319708694
Total Pages : 498 pages
Book Rating : 4.90/5 ( download)

DOWNLOAD NOW!

Download or read book Crossed Products of C*-Algebras, Topological Dynamics, and Classification written by Thierry Giordano and published by Springer. This book was released on 2018-08-28 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 attention to the classification of minimal actions by finitely generated abelian groups on the Cantor set.

Author : Aidan Sims
Publisher : Springer Nature
ISBN 13 : 3030397130
Total Pages : 163 pages
Book Rating : 4.35/5 ( download)

DOWNLOAD NOW!

Download or read book Operator Algebras and Dynamics: Groupoids, Crossed Products, and Rokhlin Dimension written by Aidan Sims and published by Springer Nature. This book was released on 2020-06-22 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the notes of the lectures given at the Advanced Course on Crossed Products, Groupoids, and Rokhlin dimension, that took place at the Centre de Recerca Matemàtica (CRM) from March 13 to March 17, 2017. The notes consist of three series of lectures. The first one was given by Dana Williams (Dartmouth College), and served as an introduction to crossed products of C*-algebras and the study of their structure. The second series of lectures was delivered by Aidan Sims (Wollongong), who gave an overview of the theory of topological groupoids (as a model for groups and group actions) and groupoid C*-algebras, with particular emphasis on the case of étale groupoids. Finally, the last series was delivered by Gábor Szabó (Copenhagen), and consisted of an introduction to Rokhlin type properties (mostly centered around the work of Hirshberg, Winter and Zacharias) with hints to the more advanced theory related to groupoids.

Author : Dana P. Williams
Publisher : American Mathematical Soc.
ISBN 13 : 9780821875186
Total Pages : 552 pages
Book Rating : 4.83/5 ( download)

DOWNLOAD NOW!

Download or read book Crossed Products of C*-algebras written by Dana P. Williams and published by American Mathematical Soc.. This book was released on with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of crossed products is extremely rich and intriguing. There are applications not only to operator algebras, but to subjects as varied as noncommutative geometry and mathematical physics. This book provides a detailed introduction to this vast subject suitable for graduate students and others whose research has contact with crossed product $C*$-algebras. in addition to providing the basic definitions and results, the main focus of this book is the fine ideal structure of crossed products as revealed by the study of induced representations via the Green-Mackey-Rieffel machine. in particular, there is an in-depth analysis of the imprimitivity theorems on which Rieffel's theory of induced representations and Morita equivalence of $C*$-algebras are based. There is also a detailed treatment of the generalized Effros-Hahn conjecture and its proof due to Gootman, Rosenberg, and Sauvageot. This book is meant to be self-contained and accessible to any graduate student coming out of a first course on operator algebras. There are appendices that deal with ancillary subjects, which while not central to the subject, are nevertheless crucial for a complete understanding of the material. Some of the appendices will be of independent interest. to view another book by this author, please visit Morita Equivalence and Continuous-Trace $C*$-Algebras.

Author : Karen R. Strung
Publisher : Springer Nature
ISBN 13 : 3030474658
Total Pages : 322 pages
Book Rating : 4.52/5 ( download)

DOWNLOAD NOW!

Download or read book An Introduction to C*-Algebras and the Classification Program written by Karen R. Strung and published by Springer Nature. This book was released on 2020-12-15 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Karen R. Strung
Publisher :
ISBN 13 : 9783030474669
Total Pages : 0 pages
Book Rating : 4.66/5 ( download)

DOWNLOAD NOW!

Download or read book An Introduction to C*-Algebras and the Classification Program written by Karen R. Strung and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Cesar E. Silva
Publisher : Springer Nature
ISBN 13 : 1071623885
Total Pages : 707 pages
Book Rating : 4.86/5 ( download)

DOWNLOAD NOW!

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

Author : Elias G. Katsoulis
Publisher : American Mathematical Soc.
ISBN 13 : 1470435454
Total Pages : 85 pages
Book Rating : 4.55/5 ( download)

DOWNLOAD NOW!

Download or read book Crossed Products of Operator Algebras written by Elias G. Katsoulis and published by American Mathematical Soc.. This book was released on 2019-04-10 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. They develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to our context. They complement their generic results with the detailed study of many important special cases. In particular they study crossed products of tensor algebras, triangular AF algebras and various associated C -algebras. They make contributions to the study of C -envelopes, semisimplicity, the semi-Dirichlet property, Takai duality and the Hao-Ng isomorphism problem. They also answer questions from the pertinent literature.

Author : 野水克己
Publisher : American Mathematical Soc.
ISBN 13 : 9780821835081
Total Pages : 152 pages
Book Rating : 4.84/5 ( download)

DOWNLOAD NOW!

Download or read book Selected Papers on Analysis and Differential Equations written by 野水克己 and published by American Mathematical Soc.. This book was released on 2003 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains translations of papers that originally appeared in the Japanese journal, Sugaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication, the Society has chosen to publish them as a volume of selected papers. The papers range over a variety of topics, including nonlinear partial differential equations, $C*$-algebras, and Schrodinger operators. The volume is suitable for graduate students and research mathematicians interested in analysis and differential equations.

Author : M. Rordam
Publisher :
ISBN 13 : 9783662048269
Total Pages : 212 pages
Book Rating : 4.64/5 ( download)

DOWNLOAD NOW!

Download or read book Classification of Nuclear C*-Algebras. Entropy in Operator Algebras written by M. Rordam and published by . This book was released on 2014-01-15 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Marcel de Jeu
Publisher : American Mathematical Soc.
ISBN 13 : 0821847473
Total Pages : 329 pages
Book Rating : 4.73/5 ( download)

DOWNLOAD NOW!

Download or read book Operator Structures and Dynamical Systems written by Marcel de Jeu and published by American Mathematical Soc.. This book was released on 2009-11-30 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a Leiden Workshop on Dynamical Systems and their accompanying Operator Structures which took place at the Lorentz Center in Leiden, The Netherlands, on July 21-25, 2008. These papers offer a panorama of selfadjoint and non-selfadjoint operator algebras associated with both noncommutative and commutative (topological) dynamical systems and related subjects. Papers on general theory, as well as more specialized ones on symbolic dynamics and complex dynamical systems, are included.