Combinatorial Set Theory of C*-algebras

• Main Author: Farah, Ilijas (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematical logic.; Functional analysis.; Operator theory.; Associative rings.; Rings (Algebra).; Mathematical Logic and Foundations.; Functional Analysis.; Operator Theory.; Associative Rings and Algebras.

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...

Table of Contents:

• 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 C*-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
• Index
• List of Symbols.