Combinatorial Set Theory of C*-Algebras

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.

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• Análise funcional e transforma
• Fundamentos da Matemática
• Lógica matemática
• Álgebra

C*-algebras;tracial von Neumann algebra;Calkin algebra;multiplier algebra;corona algebras;tracial states;representation theory of C*-algebras;combinatorial set theory;infinitary combinatorics;infinitary combinatorics of metric structures;set-theoretic axioms;norm ultraproducts;tracial ultraproducts;saturation;incompactness;automorphisms massive quotient;massive quotient algebras;quotient rigidit;graph CCR algebras