Operator Algebras and Their Modules: An Operator Space Approach (London Mathematical Society Monographs)

David P. Blecher & Christian Le Merdy

ISBN 10: 0198526598 / ISBN 13: 9780198526599

Editore: Clarendon Press, 2005

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Good++; Hardcover; Reprint Edition; Covers are still glossy with a few light handling-marks; Unblemished textblock edges; The endpapers and all text pages are clean and unmarked; The binding is excellent with a straight spine; This book will be shipped in a sturdy cardboard box with foam padding; Medium Format (8.5" - 9.75" tall); Dark blue covers with title in tan lettering; 2005, Clarendon Press; 396 pages; "Operator Algebras and Their Modules: An Operator Space Approach (London Mathematical Society Monographs)," by David P. Blecher & Christian Le Merdy.

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Dati bibliografici

• Titolo: Operator Algebras and Their Modules: An Operator Space Approach (London Mathematical Society Monographs)
• Editore: Clarendon Press
• Data di pubblicazione: 2005
• Lingua: Inglese
• ISBN 10: 0198526598
• ISBN 13: 9780198526599
• Rilegatura: Rilegato
• Condizione: Good

Descrizione articolo

Riassunto

This invaluable reference is the first to present the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text assembles the basic concepts, theory and methodologies needed to equip a beginning researcher in this area.

A major trend in modern mathematics, inspired largely by physics, is toward `noncommutative' or `quantized' phenomena. In functional analysis, this has appeared notably under the name of `operator spaces', which is a variant of Banach spaces which is particularly appropriate for solving problems concerning spaces or algebras of operators on Hilbert space arising in 'noncommutative mathematics'.

The category of operator spaces includes operator algebras, selfadjoint (that is, C*-algebras) or otherwise. Also, most of the important modules over operator algebras are operator spaces. A common treatment of the subjects of C*-algebras, nonselfadjoint operator algebras, and modules over such algebras (such as Hilbert C*-modules), together under the umbrella of operator space theory, is the main topic of the book. A general theory of operator algebras, and their modules, naturally develops out of the operator space methodology. Indeed, operator space theory is a sensitive enough medium to reflect accurately many important noncommutative phenomena. Using recent advances in the field, the book shows how the underlying operator space structure captures, very precisely, the profound relations between the algebraic and the functional analytic structures involved. The rich interplay between spectral theory, operator theory, C*-algebra and von Neumann algebra techniques, and the influx of important ideas from related disciplines, such as pure algebra, Banach space theory, Banach algebras, and abstract function theory is highlighted. Each chapter ends with a lengthy section of notes containing a wealth of additional information.

Informazioni sull?autore

Blecher won the University of Houston Research Excellence award in 1996.