Actions Of Discrete Amenable Groups On Von Neumann Algebras
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Actions Of Discrete Amenable Groups On Von Neumann Algebras
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Author : Adrian Ocneanu
language : en
Publisher: Springer
Release Date : 2006-12-08
Actions Of Discrete Amenable Groups On Von Neumann Algebras written by Adrian Ocneanu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
Classification Of Actions Of Discrete Kac Algebras On Injective Factors
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Author : Toshihiko Masuda
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-01-18
Classification Of Actions Of Discrete Kac Algebras On Injective Factors written by Toshihiko Masuda 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 2017-01-18 with Injective modules (Algebra) categories.
The authors study two kinds of actions of a discrete amenable Kac algebra. The first one is an action whose modular part is normal. They construct a new invariant which generalizes a characteristic invariant for a discrete group action, and we will present a complete classification. The second is a centrally free action. By constructing a Rohlin tower in an asymptotic centralizer, the authors show that the Connes–Takesaki module is a complete invariant.
Rohlin Flows On Von Neumann Algebras
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Author : Toshihiko Masuda
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-10-05
Rohlin Flows On Von Neumann Algebras written by Toshihiko Masuda 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 2016-10-05 with Conjugacy classes categories.
The authors will classify Rohlin flows on von Neumann algebras up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as Kawahigashi's classification of flows on the injective type II1 factor, the classification of injective type III factors due to Connes, Krieger and Haagerup and the non-fullness of type III0 factors. Several concrete examples are also studied.
Amenability
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Author : Alan L. T. Paterson
language : en
Publisher: American Mathematical Soc.
Release Date : 1988
Amenability written by Alan L. T. Paterson 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 1988 with Mathematics categories.
The subject of amenability has its roots in the work of Lebesgue at the turn of the century. In the 1940s, the subject began to shift from finitely additive measures to means. This shift is of fundamental importance, for it makes the substantial resources of functional analysis and abstract harmonic analysis available to the study of amenability. The ubiquity of amenability ideas and the depth of the mathematics involved points to the fundamental importance of the subject. This book presents a comprehensive and coherent account of amenability as it has been developed in the large and varied literature during this century. The book has a broad appeal, for it presents an account of the subject based on harmonic and functional analysis. In addition, the analytic techniques should be of considerable interest to analysts in all areas. In addition, the book contains applications of amenability to a number of areas: combinatorial group theory, semigroup theory, statistics, differential geometry, Lie groups, ergodic theory, cohomology, and operator algebras. The main objectives of the book are to provide an introduction to the subject as a whole and to go into many of its topics in some depth. The book begins with an informal, nontechnical account of amenability from its origins in the work of Lebesgue. The initial chapters establish the basic theory of amenability and provide a detailed treatment of invariant, finitely additive measures (i.e., invariant means) on locally compact groups. The author then discusses amenability for Lie groups, "almost invariant" properties of certain subsets of an amenable group, amenability and ergodic theorems, polynomial growth, and invariant mean cardinalities. Also included are detailed discussions of the two most important achievements in amenability in the 1980s: the solutions to von Neumann's conjecture and the Banach-Ruziewicz Problem. The main prerequisites for this book are a sound understanding of undergraduate-level mathematics and a knowledge of abstract harmonic analysis and functional analysis. The book is suitable for use in graduate courses, and the lists of problems in each chapter may be useful as student exercises.
Operator Algebras Quantization And Noncommutative Geometry
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Author : Robert S. Doran
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Operator Algebras Quantization And Noncommutative Geometry written by Robert S. Doran 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 2004 with Computers categories.
John von Neumann and Marshall Stone were two giants of Twentieth Century mathematics. In honor of the 100th anniversary of their births, a mathematical celebration was organized featuring developments in fields where both men were major influences. This volume contains articles from the AMS Special Session, Operator Algebras, Quantization and Noncommutative Geometry: A Centennial Celebration in Honor of John von Neumann and Marshall H. Stone. Papers range from expository and refereed and cover a broad range of mathematical topics reflecting the fundamental ideas of von Neumann and Stone. Most contributions are expanded versions of the talks and were written exclusively for this volume. Included, among Also featured is a reprint of P.R. Halmos's The Legend of John von Neumann. The book is suitable for graduate students and researchers interested in operator algebras and applications, including noncommutative geometry.
Advances In Quantum Dynamics
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Author : Geoffrey L. Price
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Advances In Quantum Dynamics written by Geoffrey L. Price 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 2003 with Mathematics categories.
This volume contains the proceedings of the conference on Advances in Quantum Dynamics. The purpose of the conference was to assess the current state of knowledge and to outline future research directions of quantum dynamical semigroups on von Neumann algebras. Since the appearance of the landmark papers by F. Murray and J. von Neumann, On the Rings of Operators, von Neumann algebras have been used as a mathematical model in the study of time evolution of quantum mechanical systems.Following the work of M. H. Stone, von Neumann, and others on the structure of one-parameter groups of unitary transformations, many researchers have made fundamental contributions to the understanding of time-reversible dynamical systems. This book deals with the mathematics of time-irreversiblesystems, also called dissipative systems. The time parameter is the half-line, and the transformations are now endomorphisms as opposed to automorphisms. For over a decade, W. B. Arveson and R. T. Powers have pioneered the effort to understand the structure of irreversible quantum dynamical systems on von Neumann algebras. Their papers in this volume serve as an excellent introduction to the theory. Also included are contributions in other areas which have had an impact on the theory, such asBrownian motion, dilation theory, quantum probability, and free probability. The volume is suitable for graduate students and research mathematicians interested in the dynamics of quantum systems and corresponding topics in the theory of operator algebras.
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Author :
language : en
Publisher: World Scientific
Release Date :
written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Lectures On Amenability
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Author : Volker Runde
language : en
Publisher: Springer
Release Date : 2004-10-14
Lectures On Amenability written by Volker Runde and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-14 with Mathematics categories.
The notion of amenability has its origins in the beginnings of modern measure theory: Does a finitely additive set function exist which is invariant under a certain group action? Since the 1940s, amenability has become an important concept in abstract harmonic analysis (or rather, more generally, in the theory of semitopological semigroups). In 1972, B.E. Johnson showed that the amenability of a locally compact group G can be characterized in terms of the Hochschild cohomology of its group algebra L^1(G): this initiated the theory of amenable Banach algebras. Since then, amenability has penetrated other branches of mathematics, such as von Neumann algebras, operator spaces, and even differential geometry. Lectures on Amenability introduces second year graduate students to this fascinating area of modern mathematics and leads them to a level from where they can go on to read original papers on the subject. Numerous exercises are interspersed in the text.
Current Topics In Operator Algebras Proceedings Of The Satellite Conference Of Icm 90
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Author : Y Nakagami
language : en
Publisher: World Scientific
Release Date : 1991-04-29
Current Topics In Operator Algebras Proceedings Of The Satellite Conference Of Icm 90 written by Y Nakagami and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-04-29 with categories.
The topics covered in this proceedings include the C* — dynamical systems, the index theory of subfactors, the noncommutative differential geometry and the quantum groups. This volume presents an overview of the present status of the theory of operator algebras, as well as an outlook for its future development.
Amenable Banach Algebras
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Author : Jean-Paul Pier
language : en
Publisher: Longman Publishing Group
Release Date : 1988
Amenable Banach Algebras written by Jean-Paul Pier and has been published by Longman Publishing Group this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Banach algebras categories.
