Completely Bounded Maps and Operator Algebras

This book, first published in 2003, is an indispensable introduction to the theory of operator spaces for graduate students and experts alike.

Vern Paulsen (Author)

9780521816694, Cambridge University Press

Hardback, published 6 February 2003

314 pages
16.1 x 23.4 x 2.1 cm, 0.53 kg

'Paulsen's book has the advantage of still being concise and staying close to the origins of the theory … the subject of operator spaces is now very well covered and has been made accessible to both the newcomer to the subject, and the specialist looking for concise references, alike. In conclusion, we quote from the cover text of [2]: 'This will be an indispensable introduction to the theory of operator spaces for all who want to know more.' We add: you surely will want to know more.' Martin Mathieu, Queen's University Belfast

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.

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.

Subject Areas: Calculus & mathematical analysis [PBK]