The theory of operator spaces is very recent and can be described as a non-commutative Banach space theory. An " operator space " is simply a Banach space with an embedding into the space B (H) of all bounded operators on a Hilbert space H. The first part of this book is an introduction with emphasis on examples that illustrate varions aspects of the theory. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C*-algebras. The third (and shortest) part of the book describes applications to non-self-adjoint operator algebras and similarity problems. In particular, the author's counterexample to the " Halmos problem " is presented, as well as work on the new concept of "length" of an operator algebra.
Graduate students and professional mathematicians interested in functional analysis, operator algebras, and theoretical physics will find that this book has much to offer.