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
8 - Biduals, injective von Neumann algebras, and C*-norms
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
We study here the maps (defined on an operator space with values in a C*-algebra) that are bounded when "tensorized" with the identity of any other C*-algebra with respect to either the minimal or the maximal tensor product. More generally, we address here several natural questions inspired by category theory, related to injectivity and projectivity of morphisms.
- Type
- Chapter
- Information
- Tensor Products of C*-Algebras and Operator SpacesThe Connes–Kirchberg Problem, pp. 161 - 179Publisher: Cambridge University PressPrint publication year: 2020