About this book
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
- 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 Mathematics and Statistics (R0)
- Print ISBN 978-1-4471-6773-0
- Online ISBN 978-1-4471-6775-4
- Series Print ISSN 1439-7382
- Series Online ISSN 2196-9922
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