Description
Book SynopsisThis book, first published in 2003, is a self-contained introduction to the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, plus some of their main applications. An indispensable introduction to the theory of operator spaces for graduate students and experts alike.
Trade Review'This book has been written by one of the leading figures in the field. the choice of the presented material has been done in a masterly manner … an excellent introduction to this theory for graduate students. It should also provide a valuable reference source for researchers in the field.' Zentralblatt für Mathematik
'The book is carefully written, proofs are often accompanied with notes helping to explain the situation.' EMS Newsletter
'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
Table of Contents1. 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.
