Combinatorial Set Theory of C*-algebras

Beschreibung

This book explores and highlights the fertile interaction between logic and operator algebras, which in recent years has led to the resolution of several long-standing open problems on C*-algebras. The interplay between logic and operator algebras (C*-algebras, in particular) is relatively young and the author is at the forefront of this interaction. The deep level of scholarship contained in these pages is evident and opens doors to operator algebraists interested in learning about the set-theoretic methods relevant to their field, as well as to set-theorists interested in expanding their view to the non-commutative realm of operator algebras. Enough background is included from both subjects to make the book a convenient, self-contained source for students.  A fair number of the exercises form an integral part of the text. They are chosen to widen and deepen the material from the corresponding chapters. Some other exercises serve as a warmup for the latter chapters.
This book explores and highlights the fertile interaction between logic and operator algebras, which in recent years has led to the resolution of several long-standing open problems on C*-algebras. The interplay between logic and operator algebras (C*-algebras, in particular) is relatively young and the author is at the forefront of this interaction. The deep level of scholarship contained in these pages is evident and opens doors to operator algebraists interested in learning about the set-theoretic methods relevant to their field, as well as to set-theorists interested in expanding their view to the non-commutative realm of operator algebras. Enough background is included from both subjects to make the book a convenient, self-contained source for students.  A fair number of the exercises form an integral part of the text. They are chosen to widen and deepen the material from the corresponding chapters. Some other exercises serve as a warmup for the latter chapters.
First book on the applications of logic and set theory to operator algebras Presents dramatic progress on the resolution of several long-standing problems on C*-algebras Provides a concise guide to the relevant theory of sets and C*-algebras

Autor*in

Ilijas Farah

Themen in »Combinatorial Set Theory of C*-algebras«

C*-algebras Calkin algebra combinatorial set theory corona algebras tracial states irreducible representations infinitary combinatorics set-theoretic axioms multiplier algebra automorphisms massive quotient axiomatic set theory Abelian C*-algebras Aacai descriptive set theory

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“The target audience is graduate students with background in functional analysis and rudiments of mathematical logic, but the book can be read, with some additional effort, by a well-motivated student who has never encountered either of the two subjects. The book can be used as a blueprint to design a graduate-level course in the applications of set theory to operator algebras, and contains hints for future directions of research.” (Alessandro Vignati, Mathematical Reviews, February, 2021)

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