Tensor Products of C*-Algebras and Operator Spaces

The Connes-Kirchberg Problem

AvGilles Pisier

Häftad, Engelska, 2020

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Beskrivning

Based on the author's university lecture courses, this book presents the many facets of one of the most important open problems in operator algebra theory. Central to this book is the proof of the equivalence of the various forms of the problem, including forms involving C*-algebra tensor products and free groups, ultraproducts of von Neumann algebras, and quantum information theory. The reader is guided through a number of results (some of them previously unpublished) revolving around tensor products of C*-algebras and operator spaces, which are reminiscent of Grothendieck's famous Banach space theory work. The detailed style of the book and the inclusion of background information make it easily accessible for beginning researchers, Ph.D. students, and non-specialists alike.

Produktinformation

Utgivningsdatum:2020-02-27
Mått:153 x 227 x 27 mm
Vikt:700 g
Format:Häftad
Språk:Engelska
Serie:London Mathematical Society Student Texts
Antal sidor:494
Förlag:Cambridge University Press
ISBN:9781108749114

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Mer om författaren

Gilles Pisier is Emeritus Professor at Sorbonne Université and Distinguished Professor at Texas A & M University. He is the author of several books, including Introduction to Operator Space Theory (Cambridge, 2003) and Martingales in Banach Spaces (Cambridge, 2016). His multiple awards include the Salem prize in 1979 and the Ostrowski Prize in 1997, and he was the plenary speaker at the International Congress of Mathematicians in 1998.

Recensioner i media

'This is a very rich and detailed monograph on an enormously important subject. It is written in the crystal clear and elegant style that is the hallmark of its author, and it offers a lot of information to specialists and novices alike. The book will certainly become an authoritative guide.' Dirk Werner, London Mathematical Society Student Texts

Innehållsförteckning

Introduction; 1. Completely bounded and completely positive maps: basics; 2. Completely bounded and completely positive maps: a tool kit; 3. C*-algebras of discrete groups; 4. C*-tensor products; 5. Multiplicative domains of c.p. maps; 6. Decomposable maps; 7. Tensorizing maps and functorial properties; 8. Biduals, injective von Neumann algebras and C*-norms; 9. Nuclear pairs, WEP, LLP and QWEP; 10. Exactness and nuclearity; 11. Traces and ultraproducts; 12. The Connes embedding problem; 13. Kirchberg's conjecture; 14. Equivalence of the two main questions; 15. Equivalence with finite representability conjecture; 16. Equivalence with Tsirelson's problem; 17. Property (T) and residually finite groups. Thom's example; 18. The WEP does not imply the LLP; 19. Other proofs that C(n) < n. Quantum expanders; 20. Local embeddability into ${\mathscr{C}}$ and non-separability of $(OS_n, d_{cb})$; 21. WEP as an extension property; 22. Complex interpolation and maximal tensor product; 23. Haagerup's characterizations of the WEP; 24. Full crossed products and failure of WEP for $\mathscr{B}\otimes_{\min}\mathscr{B}$; 25. Open problems; Appendix. Miscellaneous background; References; Index.