The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms
The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms

Author: Gilles Pisier

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 119

ISBN-13: 082180474X

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In the recently developed duality theory of operator spaces, bounded operators are replaced by 'completely bounded' ones, isomorphism by 'complete isomorphisms' and Banach spaces by 'operator spaces'. This allows for distinguishing between the various ways in which a given Banach space can be embedded isometrically into [italic capital]B([italic capital]H) (with H being Hilbert). One of the main results is the observation that there is a central object in this class: there is a unique self dual Hilbertian operator space (which we denote by [italic capitals]OH) which seems to play the same central role in the category of operator spaces that Hilbert spaces play in the category of Banach spaces.

Completely Bounded Maps and Operator Algebras
Completely Bounded Maps and Operator Algebras

Author: Vern Paulsen

Publisher: Cambridge University Press

Published: 2002

Total Pages: 316

ISBN-13: 9780521816694

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In this book, first published in 2003, the reader is provided with a tour of the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, together with some of their main applications. The author assumes only that the reader has a basic background in functional analysis, and the presentation is self-contained and paced appropriately for graduate students new to the subject. Experts will also want this book for their library since the author illustrates the power of methods he has developed with new and simpler proofs of some of the major results in the area, many of which have not appeared earlier in the literature. An indispensable introduction to the theory of operator spaces for all who want to know more.

Quantum Functional Analysis
Quantum Functional Analysis

Author: Aleksandr I︠A︡kovlevich Khelemskiĭ

Publisher: American Mathematical Soc.

Published: 2010

Total Pages: 264

ISBN-13: 082185254X

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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.

Introduction to Operator Space Theory
Introduction to Operator Space Theory

Author: Gilles Pisier

Publisher: Cambridge University Press

Published: 2003-08-25

Total Pages: 492

ISBN-13: 9780521811651

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An introduction to the theory of operator spaces, emphasising applications to C*-algebras.

Quantum Potential Theory
Quantum Potential Theory

Author: Philippe Biane

Publisher: Springer Science & Business Media

Published: 2008-09-23

Total Pages: 467

ISBN-13: 3540693645

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This book offers the revised and completed notes of lectures given at the 2007 conference, "Quantum Potential Theory: Structures and Applications to Physics." These lectures provide an introduction to the theory and discuss various applications.

Operator Theory in Harmonic and Non-commutative Analysis
Operator Theory in Harmonic and Non-commutative Analysis

Author: Joseph A. Ball

Publisher: Springer

Published: 2014-06-21

Total Pages: 260

ISBN-13: 3319062662

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This book contains the proceedings of the 23rd International Workshop on Operator Theory and its Applications (IWOTA 2012), which was held at the University of New South Wales (Sydney, Australia) from 16 July to 20 July 2012. It includes twelve articles presenting both surveys of current research in operator theory and original results.