Completely Bounded Maps and Operator Algebras
Completely Bounded Maps and Operator Algebras
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$165.00
USDIn this book, first published in 2003, the reader is provided with a tour of the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, together with some of their main applications. The author assumes only that the reader has a basic background in functional analysis, and the presentation is self-contained and paced appropriately for graduate students new to the subject. Experts will also want this book for their library since the author illustrates the power of methods he has developed with new and simpler proofs of some of the major results in the area, many of which have not appeared earlier in the literature. An indispensable introduction to the theory of operator spaces for all who want to know more.
- Self-contained
- Author is an excellent expositor
- First real introduction to the subject for graduate students
Reviews & endorsements
"Although it contains deep and advanced results on operator spaces and their applications, the book is essentially self-contained and accessible to anyone with a basic knowledge in general functional analysis and C*-algebras." Mathematical Reviews
Product details
December 2004Adobe eBook Reader
9780511054709
0 pages
0kg
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- 1. Introduction
- 2. Positive maps
- 3. Completely positive maps
- 4. Dilation theorems
- 5. Commuting contractions
- 6. Completely positive maps into Mn
- 7. Arveson's extension theorems
- 8. Completely bounded maps
- 9. Completely bounded homomorphisms
- 10. Polynomially bounded operators
- 11. Applications to K-spectral sets
- 12. Tensor products and joint spectral sets
- 13. Operator systems and operator spaces
- 14. An operator space bestiary
- 15. Injective envelopes
- 16. Multipliers and operator algebras
- 17. Completely bounded multilinear maps
- 18. Applications of operator algebras
- 19. Similarity and factorization degree.
