Book contents
- Frontmatter
- Contents
- Introduction
- 1 Completely bounded and completely positive maps
- 2 Completely bounded and completely positive maps
- 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, 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
- 18 The WEP does not imply the LLP
- 19 Other proofs that C(n)
- 20
Local embeddability into C and nonseparability of (OSn, dcb)- 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 B ⊗min B- 25
Open problems- Appendix
Miscellaneous backgroundReferencesIndex - 20
21 - WEP as an extension property
Published online by Cambridge University Press: 10 February 2020
Book contents
- Frontmatter
- Contents
- Introduction
- 1 Completely bounded and completely positive maps
- 2 Completely bounded and completely positive maps
- 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, 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
- 18 The WEP does not imply the LLP
- 19 Other proofs that C(n)
- 20 Local embeddability into C and nonseparability of (OSn, dcb)
- 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 B ⊗min B
- 25 Open problems
- Appendix Miscellaneous background
- References
- Index
Summary
This chapter is an excursion into what could be called the local theoryof operator spaces. Here the main interest is on finite dimensional operator spaces and the degree of isomorphism of the various spaces is estimated using the c.b. analogue of the Banach-Mazur distance from Banach space theory. The main result is that the metric space formed of all the n-dimensional operator spaces equipped with the latter cb-distance is non separable for any n>2. This is in sharp contrast with the Banach space analogue which is a compact metric space.
- Type
- Chapter
- Information
- Tensor Products of C*-Algebras and Operator SpacesThe Connes–Kirchberg Problem, pp. 358 - 365Publisher: Cambridge University PressPrint publication year: 2020