Author: Adrian OcneanuPublisher: Springer
ISBN: 3540395792
Category : Mathematics
Languages : en
Pages : 120
Book Description
Actions of Discrete Amenable Groups on von Neumann Algebras
Author: Adrian OcneanuPublisher: Springer
ISBN: 3540395792
Category : Mathematics
Languages : en
Pages : 120
Book Description
Action of Discrete Amenable Groups on Von Neumann Algebras
Author: Adrian OcneanuClassification of Actions of Discrete Kac Algebras on Injective Factors
Author: Toshihiko MasudaPublisher: American Mathematical Soc.
ISBN: 1470420554
Category : Injective modules (Algebra)
Languages : en
Pages : 118
Book Description
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
Author: Toshihiko MasudaPublisher: American Mathematical Soc.
ISBN: 1470420163
Category : Conjugacy classes
Languages : en
Pages : 111
Book Description
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.
Author: Amenability
Author: Alan L. T. PatersonPublisher: American Mathematical Soc.
ISBN: 0821809857
Category : Mathematics
Languages : en
Pages : 474
Book Description
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.
Subfactors: Proceedings Of The Taniguchi Symposium On Operator Algebras
Author: Huzihiro ArakiPublisher: World Scientific
ISBN: 981455071X
Category :
Languages : en
Pages : 306
Book Description
The theory of subfactors of von Neumann algebras made an amazing development in the past ten years or so. In order to appraise the present state of the art in subfactor theory and to look for promising directions of future research, the workshop was organised. This workshop gives an overview of the foremost developments in subfactor theory and related topics.
Operator Structures and Dynamical Systems
Author: Marcel de JeuPublisher: American Mathematical Soc.
ISBN: 0821847473
Category : Mathematics
Languages : en
Pages : 329
Book Description
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.
Groups with the Haagerup Property
Author: Pierre-Alain CherixPublisher: Springer Science & Business Media
ISBN: 9783764365981
Category : Mathematics
Languages : en
Pages : 144
Book Description
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.
Operator Algebras, Quantization, and Noncommutative Geometry
Author: Robert S. DoranPublisher: American Mathematical Soc.
ISBN: 0821834029
Category : Computers
Languages : en
Pages : 434
Book Description
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.