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Invitation To C*-algebras And Topological Dynamics

Invitation To C*-algebras And Topological Dynamics
Author: Jun Tomiyama
Publisher: World Scientific
Total Pages: 179
Release: 1987-10-01
Genre: Mathematics
ISBN: 9814507792

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This book is an exposition on the interesting interplay between topological dynamics and the theory of C*-algebras. Researchers working in topological dynamics from various fields in mathematics are becoming more and more interested in this kind of algebraic approach of dynamics. This book is designed to present to the readers the subject in an elementary way, including also results of recent developments.


Invitation to C*-algebras and Topological Dynamics

Invitation to C*-algebras and Topological Dynamics
Author: Jun Tomiyama
Publisher: World Scientific
Total Pages: 180
Release: 1987
Genre: Science
ISBN: 9789971503383

Download Invitation to C*-algebras and Topological Dynamics Book in PDF, ePub and Kindle

This book is an exposition on the interesting interplay between topological dynamics and the theory of C*-algebras. Researchers working in topological dynamics from various fields in mathematics are becoming more and more interested in this kind of algebraic approach of dynamics. This book is designed to present to the readers the subject in an elementary way, including also results of recent developments.


Crossed Products of C*-Algebras, Topological Dynamics, and Classification

Crossed Products of C*-Algebras, Topological Dynamics, and Classification
Author: Thierry Giordano
Publisher: Springer
Total Pages: 498
Release: 2018-08-28
Genre: Mathematics
ISBN: 3319708694

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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.


$C^*$-Algebras of Homoclinic and Heteroclinic Structure in Expansive Dynamics

$C^*$-Algebras of Homoclinic and Heteroclinic Structure in Expansive Dynamics
Author: Klaus Thomsen
Publisher: American Mathematical Soc.
Total Pages: 138
Release: 2010-06-11
Genre: Mathematics
ISBN: 0821846922

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The author unifies various constructions of $C^*$-algebras from dynamical systems, specifically, the dimension group construction of Krieger for shift spaces, the corresponding constructions of Wagoner and Boyle, Fiebig and Fiebig for countable state Markov shifts and one-sided shift spaces, respectively, and the constructions of Ruelle and Putnam for Smale spaces. The general setup is used to analyze the structure of the $C^*$-algebras arising from the homoclinic and heteroclinic equivalence relations in expansive dynamical systems, in particular, expansive group endomorphisms and automorphisms and generalized 1-solenoids. For these dynamical systems it is shown that the $C^*$-algebras are inductive limits of homogeneous or sub-homogeneous algebras with one-dimensional spectra.


Operator Structures and Dynamical Systems

Operator Structures and Dynamical Systems
Author: Marcel de Jeu
Publisher: American Mathematical Soc.
Total Pages: 329
Release: 2009-11-30
Genre: Mathematics
ISBN: 0821847473

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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.


Operator Algebras and Operator Theory

Operator Algebras and Operator Theory
Author: Liming Ge
Publisher: American Mathematical Soc.
Total Pages: 416
Release: 1998
Genre: Mathematics
ISBN: 0821810936

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This volume contains the proceedings from the International Conference on Operator Algebras and Operator Theory held at the East China Normal University in Shanghai (China). Participants in the conference ranged from graduate students to postdocs to leading experts who came from around the world. Topics covered were $C*$-algebras, von Neumann algebras, non-self-adjoint operator algebras, wavelets, operator spaces and other related areas. This work consists of contributions from invited speakers and some mathematicians who were unable to attend. It presents important mathematical ideas while maintaining the uniqueness and excitement of this very successful event.


Crossed Products of C*-Algebras, Topological Dynamics, and Classification

Crossed Products of C*-Algebras, Topological Dynamics, and Classification
Author: Thierry Giordano
Publisher:
Total Pages: 498
Release: 2018
Genre: Functional analysis
ISBN: 9783319708706

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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.


Stochastic Processes, Statistical Methods, and Engineering Mathematics

Stochastic Processes, Statistical Methods, and Engineering Mathematics
Author: Anatoliy Malyarenko
Publisher: Springer Nature
Total Pages: 907
Release: 2023-01-26
Genre: Mathematics
ISBN: 3031178203

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The goal of the 2019 conference on Stochastic Processes and Algebraic Structures held in SPAS2019, Västerås, Sweden, from September 30th to October 2nd 2019, was to showcase the frontiers of research in several important areas of mathematics, mathematical statistics, and its applications. The conference was organized around the following topics 1. Stochastic processes and modern statistical methods,2. Engineering mathematics,3. Algebraic structures and their applications. The conference brought together a select group of scientists, researchers, and practitioners from the industry who are actively contributing to the theory and applications of stochastic, and algebraic structures, methods, and models. The conference provided early stage researchers with the opportunity to learn from leaders in the field, to present their research, as well as to establish valuable research contacts in order to initiate collaborations in Sweden and abroad. New methods for pricing sophisticated financial derivatives, limit theorems for stochastic processes, advanced methods for statistical analysis of financial data, and modern computational methods in various areas of applied science can be found in this book. The principal reason for the growing interest in these questions comes from the fact that we are living in an extremely rapidly changing and challenging environment. This requires the quick introduction of new methods, coming from different areas of applied science. Advanced concepts in the book are illustrated in simple form with the help of tables and figures. Most of the papers are self-contained, and thus ideally suitable for self-study. Solutions to sophisticated problems located at the intersection of various theoretical and applied areas of the natural sciences are presented in these proceedings.


Operator Algebra and Dynamics

Operator Algebra and Dynamics
Author: Toke M. Carlsen
Publisher: Springer Science & Business Media
Total Pages: 343
Release: 2013-12-03
Genre: Mathematics
ISBN: 3642394590

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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.


$C^*$-Algebras: 1943-1993

$C^*$-Algebras: 1943-1993
Author:
Publisher: American Mathematical Soc.
Total Pages: 434
Release: 1994
Genre: C*-algebras
ISBN: 0821851756

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