Operator Spaces (London Mathematical Society Monographs) - Hardcover

Effros, Edward G.; Ruan, Zhong-Jin

Hardcover

ISBN 10: 0198534825 ISBN 13: 9780198534822

Publisher: Oxford University Press, 2000

Synopsis

Operator space theory provides a synthesis of Banach space theory with the non-commuting 'quantum' variables of operator algebra theory, and it has led to exciting new approaches in both disciplines. The authors begin by giving completely elementary proofs of the basic representation theorems for abstract operator spaces and their mappings. This is followed by a discussion of tensor products and the analogue of Grothendieck's approximation property. In the next section, the operator space analogues of the nuclear, integral and absolutely summing mappings are discussed. In what is perhaps the deepest part of the book, the authors present the remarkable 'non-classical' phenomena that occur when one considers local reflexivity and exactness for operator spaces. They have included the recent proof that, in contrast to C*-algebras themselves, C*-algebraic duals are always locally reflexive. In the final section of the book, the authors consider applications to non-commutative harmonic analysis and non-self-adjoint operator algebra theory.

About this title

About the Author

Professor E G Effros Department of Mathematics University of California LOS ANGELES, CA 90024-1555 USA Professor Z-J Ruan Department of Mathematics University of Illinois Urbana, IL 61801 USA

Edition details

• Publisher: Oxford University Press
• Publication date: 2000
• Language: English
• ISBN 10: 0198534825
• ISBN 13: 9780198534822
• Binding: Hardcover
• Number of pages: 380