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An Invitation to von Neumann Algebras

  • V. S. Sunder

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. V. S. Sunder
    Pages 1-18
  3. V. S. Sunder
    Pages 36-83
  4. V. S. Sunder
    Pages 114-160
  5. Back Matter
    Pages 161-171

About this book

Introduction

Why This Book: The theory of von Neumann algebras has been growing in leaps and bounds in the last 20 years. It has always had strong connections with ergodic theory and mathematical physics. It is now beginning to make contact with other areas such as differential geometry and K-Theory. There seems to be a strong case for putting together a book which (a) introduces a reader to some of the basic theory needed to appreciate the recent advances, without getting bogged down by too much technical detail; (b) makes minimal assumptions on the reader's background; and (c) is small enough in size to not test the stamina and patience of the reader. This book tries to meet these requirements. In any case, it is just what its title proclaims it to be -- an invitation to the exciting world of von Neumann algebras. It is hoped that after perusing this book, the reader might be tempted to fill in the numerous (and technically, capacious) gaps in this exposition, and to delve further into the depths of the theory. For the expert, it suffices to mention here that after some preliminaries, the book commences with the Murray - von Neumann classification of factors, proceeds through the basic modular theory to the III). classification of Connes, and concludes with a discussion of crossed-products, Krieger's ratio set, examples of factors, and Takesaki's duality theorem.

Keywords

integration minimum operator operator theory

Authors and affiliations

  • V. S. Sunder
    • 1
  1. 1.Indian Statistical InstituteNew DelhiIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-8669-8
  • Copyright Information Springer-Verlag New York 1987
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96356-3
  • Online ISBN 978-1-4613-8669-8
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site