Combinatorial set theory of C*-Algebras Ilijas Farah

Format:

Book

Author/Creator:

Farah, Ilijas, 1966- Author.

Series:

Springer monographs in mathematics 2196-9922

Language:

English

Subjects (All):

C*-algebras.

Combinatorial set theory.

Physical Description:

1 online resource

Edition:

Second edition

Place of Publication:

Cham Springer [2026]

Summary:

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 author is at the forefront of research on the interplay between logic and operator algebras (C*-algebras, in particular). The deep level of scholarship contained in these pages 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 this book a convenient, self-contained source for students. Exercises form an integral part of the text. They widen and deepen the material from the corresponding chapters. Other exercises serve as a warmup for the latter chapters. This second edition furthers the aims of the first, improving proofs and providing new insights into the relationship between logic and operator algebras. It has been expanded, adding new lemmas, definitions, propositions, and exercises. The book provides a comprehensive analysis of ultraproducts of tracial von Neumann algebras. It also introduces Kirchberg's epsilon-test for ultraproducts and reduced products, along with its strict strengthening

Contents:

Preface

Part I C*-algebras

1. C*-algebras, Abstract and Concrete

2. Examples and Constructions of C*-algebras

3. Representations of C*-algebras

4. Tracial States and Representations of C*-algebras

5. Irreducible Representations of C*-algebras

Part II Set Theory and Nonseparable C*-algebras

6. Infinitary Combinatorics, I

7. Infinitary Combinatorics, II: The Metric Case

8. Additional Set-Theoretic Axioms

9. Set Theory and Quotients

10. Constructions of Nonseparable C*-algebras, I: Graph CCR Algebras

11. Constructions of Nonseparable C*-algebras, II

Part III Massive Quotient algebras

12. The Calkin Algebra

13. Multiplier Algebras and Coronas

14. Gaps and Incompactness

15. Degree-1 Saturation

16. Full Saturation

17. Automorphisms of Massive Quotient C*-Algebras.-Part IV Appendices

A. Axiomatic Set Theory

B. Descriptive Set Theory

C. Functional Analysis

D. Model Theory

References

List of Symbols

Index

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (SpringerLink, viewed June 24, 2026)

ISBN:

9783032086105

3032086108

OCLC:

1599128754

Access Restriction:

Restricted for use by site license