Interpreting "quantized coefficients" as finite rank operators in a fixed Hilbert space allows the author to replace matrix computations with algebraic techniques of module theory and tensor products, thus achieving a more invariant approach to the subject. Series: University Lecture Series. Num Pages: 257 pages, Illustrations. BIC Classification: PBKF. Category: (P) Professional & Vocational. Dimension: 229 x 152. . . 2010. 1st. Paperback. . . . .

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Bibliographic Details

Title: Quantum Functional Analysis: Non-coordinate Approach (University Lecture Series, Vol. 56)
Publisher: American Mathematical Society
Publication Date: 2010
Language: English
ISBN 10: 082185254X
ISBN 13: 9780821852545
Binding: Soft cover
Condition: New

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Synopsis

This book contains a systematic presentation of quantum functional analysis, a mathematical subject also known as operator space theory. Created in the 1980s, it nowadays is one of the most prominent areas of functional analysis, both as a field of active research and as a source of numerous important applications. The approach taken in this book differs significantly from the standard approach used in studying operator space theory. Instead of viewing "quantized coefficients" as matrices in a fixed basis, in this book they are interpreted as finite rank operators in a fixed Hilbert space. This allows the author to replace matrix computations with algebraic techniques of module theory and tensor products, thus achieving a more invariant approach to the subject. The book can be used by graduate students and research mathematicians interested in functional analysis and related areas of mathematics and mathematical physics. Prerequisites include standard courses in abstract algebra and functional analysis.

Review

This book is highly recommended to mathematicians who wish to become acquainted with the research field of operator spaces, operator modules and operator algebras. --Mathematical Reviews

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