Monotone Complete C*-algebras and Generic Dynamics

1. Front Matter

   Pages i-xi

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2. Introduction

   • Kazuyuki Saitô, J. D. Maitland Wright

   Pages 1-6

3. Order Fundamentals

   • Kazuyuki Saitô, J. D. Maitland Wright

   Pages 7-48

4. Classification and Invariants

   • Kazuyuki Saitô, J. D. Maitland Wright

   Pages 49-61

5. Commutative Algebras: Constructions and Classifications

   • Kazuyuki Saitô, J. D. Maitland Wright

   Pages 63-89

6. Convexity and Representations

   • Kazuyuki Saitô, J. D. Maitland Wright

   Pages 91-140

7. Generic Dynamics

   • Kazuyuki Saitô, J. D. Maitland Wright

   Pages 141-180

8. Constructing Monotone Complete C ^∗-Algebras

   • Kazuyuki Saitô, J. D. Maitland Wright

   Pages 181-218

9. Envelopes, Completions and AW ^∗-Algebras

   • Kazuyuki Saitô, J. D. Maitland Wright

   Pages 219-245

10. Back Matter

    Pages 247-257

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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.

• 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

“The monograph under review, written by two leading experts in the field, is an invaluable contribution to the study and dissemination of m.c. C*-algebras. It provides, in a historic perspective, an updated and thorough description of the recent research on this broad class of C*-algebras, highlighting its important connections with topology, logic, and ergodic theory. ... the present book is an excellent addition to the operator algebras literature, covering for the first time the two themes advertised in the title.” (Florin P. Boca, zbMATH 1382.46003, 2018)

• Sendai, Japan

  Kazuyuki Saitô

• University of Aberdeen, Aberdeen, United Kingdom

  J. D. Maitland Wright

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