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Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.
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Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.
Produktdetails
- Produktdetails
- Verlag: Cambridge University Press
- Seitenzahl: 494
- Erscheinungstermin: 2. April 2020
- Englisch
- Abmessung: 226mm x 163mm x 25mm
- Gewicht: 680g
- ISBN-13: 9781108749114
- ISBN-10: 1108749119
- Artikelnr.: 58600878
- Verlag: Cambridge University Press
- Seitenzahl: 494
- Erscheinungstermin: 2. April 2020
- Englisch
- Abmessung: 226mm x 163mm x 25mm
- Gewicht: 680g
- ISBN-13: 9781108749114
- ISBN-10: 1108749119
- Artikelnr.: 58600878
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.
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.
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.
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.
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.