Monotone Complete C*-algebras and Generic Dynamics

Beschreibung

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 fromthe basics to recent advances. The prerequisites are a grounding in functional analysis, some point set topology and an elementary knowledge of C*-algebras.
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.
Unique in presenting the modern theory of monotone complete C*-algebras Gives a self-contained introduction to generic dynamics Explains the new classification theory introducing spectroids and classification semigroups Includes supplementary material: sn.pub/extras

Autor*in

Kazuyuki Saitô

Themen in »Monotone Complete C*-algebras and Generic Dynamics«

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

Stimmen zu »Monotone Complete C*-algebras and Generic Dynamics«

“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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