Introduction to Operator Space Theory
Introduction to Operator Space Theory
Author:
Gilles Pisier, Texas A & M University and Université de Paris VI (Pierre et Marie Curie)
Published:
August 2003
Availability:
Available
Format:
Paperback
ISBN:
9780521811651
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The first part of this book is an introduction with emphasis on examples that illustrate the theory of operator spaces. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C* algebras. The third part of the book describes applications to non self-adjoint operator algebras and similarity problems. The author's counterexample to the "Halmos problem" is presented, along with work on the new concept of "length" of an operator algebra.
- Authoritative
- Up-to-date
- Suitable for graduate students
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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.
