Completely Bounded Maps and Operator Algebras (Cambridge Studies in Advanced Mathematics, Series Number 78)

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.

In this book 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 presentation is appropriate to graduate students and experts alike. The author assumes only that the reader has a basic background in functional analysis, but also provides new and simpler proofs of some of the major results in the area, many of which have not appeared earlier in the literature.