Completely Bounded Maps and Operator Algebras

Completely Bounded Maps and Operator Algebras

This book tours the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, along with some of their main applications. It requires only a basic background in functional analysis. The presentation is self-contained and paced appropriately for graduate students new to the subject. Experts will appreciate how 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 indispensible introduction to the theory of operator spaces.


"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

'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