Completely bounded maps and operator algebras
Author(s)
Bibliographic Information
Completely bounded maps and operator algebras
（Cambridge studies in advanced mathematics, 78）
Cambridge University Press, 2002
- : hardback
Available at / 51 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hardbackS||CSAM||7803001582
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Note
Includes bibliographical references (p. 285-295) and index
Description and Table of Contents
Description
In 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.
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.
by "Nielsen BookData"