Introduction to Operator Space Theory [Paperback]

An introduction to the theory of operator spaces, emphasising applications to C*-algebras.The theory of operator spaces is very recent and can be described as a non-commutative Banach space theory. The first part of this book provides an introduction with emphasis on examples that illustrate the theory. The second part discusses applications to C*-algebras, with a systematic exposition of tensor products of C* algebras. The final part describes applications to non self-adjoint operator algebras, and similarity problems. Graduate students and professional mathematicians interested in functional analysis, operator algebras and theoretical physics will find that this book has much to offer.The theory of operator spaces is very recent and can be described as a non-commutative Banach space theory. The first part of this book provides an introduction with emphasis on examples that illustrate the theory. The second part discusses applications to C*-algebras, with a systematic exposition of tensor products of C* algebras. The final part describes applications to non self-adjoint operator algebras, and similarity problems. Graduate students and professional mathematicians interested in functional analysis, operator algebras and theoretical physics will find that this book has much to offer.The first part of this book is an introduction with emphasis on examples that illustrate the theory of operator spaces. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C* algebras. The third part of the book describes applications to non self-adjoint operator algebras and similarity problems. The author's counterexample to the Halmos problem is presented, along with work on the new concept of length of an operator algebra.Part I. Introduction to Operator Spaces: 1. Completely bounded maps; 2. Minimal tensor product; 3. Minimal and maximal operator space structures on a Banach space; 4. Projective tensor product; 5. The Haal³@