Introduction to Operator Space Theory

Table of Contents

Part I. Introduction to Operator Spaces:
1. Completely bounded maps
2. Minimal tensor product
3. Minimal and maximal operator space structures on a Banach space
4. Projective tensor product
5. The Haagerup tensor product
6. Characterizations of operator algebras
7. The operator Hilbert space
8. Group C*-algebras
9. Examples and comments
10. Comparisons
Part II. Operator Spaces and C*-tensor products:
11. C*-norms on tensor products
12. Nuclearity and approximation properties
13. C*
14. Kirchberg's theorem on decomposable maps
15. The weak expectation property
16. The local lifting property
17. Exactness
18. Local reflexivity
19. Grothendieck's theorem for operator spaces
20. Estimating the norms of sums of unitaries
21. Local theory of operator spaces
22. B(H) * B(H)
23. Completely isomorphic C*-algebras
24. Injective and projective operator spaces
Part III. Operator Spaces and Non Self-Adjoint Operator Algebras:
25. Maximal tensor products and free products of non self-adjoint operator algebras
26. The Blechter-Paulsen factorization
27. Similarity problems
28. The Sz-nagy-halmos similarity problem
Solutions to the exercises
References.

Look Inside

• Front Matter (215 KB)
• Table of Contents (121 KB)
• Copyright Information Page (125 KB)
• Index (141 KB)
• Marketing Excerpt (228 KB)
• Marketing Sample (175 KB)