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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 -algebra s 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.

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Introduction.- Order Fundamentals.- Classification and Invariants.- Commutative Algebras: Constructions and Classifications.- Convexity and Representations.- Generic Dynamics.- Constructing Monotone Complete C -algebras.- Envelopes, Completions and AW -algebras.

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"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)

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