Monotone Complete C*-algebras and Generic Dynamics

  • Kazuyuki Saitô
  • J. D. Maitland Wright

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Kazuyuki Saitô, J. D. Maitland Wright
    Pages 1-6
  3. Kazuyuki Saitô, J. D. Maitland Wright
    Pages 7-48
  4. Kazuyuki Saitô, J. D. Maitland Wright
    Pages 49-61
  5. Kazuyuki Saitô, J. D. Maitland Wright
    Pages 63-89
  6. Kazuyuki Saitô, J. D. Maitland Wright
    Pages 91-140
  7. Kazuyuki Saitô, J. D. Maitland Wright
    Pages 141-180
  8. Kazuyuki Saitô, J. D. Maitland Wright
    Pages 181-218
  9. Kazuyuki Saitô, J. D. Maitland Wright
    Pages 219-245
  10. Back Matter
    Pages 247-257

About this book

Introduction

This monograph is about monotone complete C*-algebras, their properties and the new classification theory. A self-contained introduction to generic dynamics is also included because of its important connections to these algebras.

Our knowledge and understanding of monotone complete C*-algebras has been transformed in recent years. This is a very exciting stage in their development, with much discovered but with many mysteries to unravel. This book is intended to encourage graduate students and working mathematicians to attack some of these difficult questions.

Each bounded, upward directed net of real numbers has a limit. Monotone complete algebras of operators have a similar property. In particular, every von Neumann algebra is monotone complete but the converse is false.

Written by major contributors to this field, Monotone Complete C*-algebras and Generic Dynamics takes readers from the basics to recent advances. The prerequisites are a grounding in functional analysis, some point set topology and an elementary knowledge of C*-algebras.

Keywords

C*-algebras Monotone Complete AW*-algebras Operator System Regular (σ-)completion Operator Space Classification Semigroup Spectroid Classification of Factors Wild Factors Small Algebras Injective Envelope Generic Dynamics Automorphisms Automorphism Group Action of Groups Free Actions Ergodic Actions Orbit Equivalence Cross-product Algebras

Authors and affiliations

  • Kazuyuki Saitô
    • 1
  • J. D. Maitland Wright
    • 2
  1. 1.SendaiJapan
  2. 2.University of AberdeenAberdeenUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-6775-4
  • Copyright Information Springer-Verlag London 2015
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-6773-0
  • Online ISBN 978-1-4471-6775-4
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • About this book
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