Completely Bounded Maps and Operator Algebras PDF Download

Author: Vern Paulsen
Publisher: Cambridge University Press
ISBN: 9780521816694
Category : Mathematics
Languages : en
Pages : 316

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Table of contents

Author: Erling Størmer
Publisher: Springer Science & Business Media
ISBN: 3642343694
Category : Mathematics
Languages : en
Pages : 135

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Book Description
This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps. The text examines the maps’ positivity properties, as well as their associated linear functionals together with their density operators. It features special sections on extremal positive maps and Choi matrices. In sum, this is a vital publication that covers a full spectrum of matters relating to positive linear maps, of which a large proportion is relevant and applicable to today’s quantum information theory. The latter sections of the book present the material in finite dimensions, while the text as a whole appeals to a wider and more general readership by keeping the mathematics as elementary as possible throughout.

Author: Gilles Pisier
Publisher: Springer
ISBN: 3540445633
Category : Mathematics
Languages : en
Pages : 210

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Book Description
These notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C* -algebras and the third one with the disc algebra. We describe them in detail in the introduction which follows. This volume is devoted to the background necessary to understand these three problems, to the solutions that are known in some special cases and to numerous related concepts, results, counterexamples or extensions which their investigation has generated. While the three problems seem different, it is possible to place them in a common framework using the key concept of "complete boundedness", which we present in detail. Using this notion, the three problems can all be formulated as asking whether "boundedness" implies "complete boundedness" for linear maps satisfying certain additional algebraic identities.

Author: Vern I. Paulsen
Publisher:
ISBN:
Category : Analytic functions
Languages : en
Pages : 214

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Author: Gilles Pisier
Publisher: Cambridge University Press
ISBN: 9780521811651
Category : Mathematics
Languages : en
Pages : 492

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

Author: Israel Gohberg
Publisher: American Mathematical Soc.
ISBN: 9780821886502
Category : Mathematics
Languages : en
Pages : 402

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Author: Nathanial Patrick Brown
Publisher: American Mathematical Soc.
ISBN: 0821843818
Category : Mathematics
Languages : en
Pages : 530

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Book Description
$\textrm{C}*$-approximation theory has provided the foundation for many of the most important conceptual breakthroughs and applications of operator algebras. This book systematically studies (most of) the numerous types of approximation properties that have been important in recent years: nuclearity, exactness, quasidiagonality, local reflexivity, and others. Moreover, it contains user-friendly proofs, insofar as that is possible, of many fundamental results that were previously quite hard to extract from the literature. Indeed, perhaps the most important novelty of the first ten chapters is an earnest attempt to explain some fundamental, but difficult and technical, results as painlessly as possible. The latter half of the book presents related topics and applications--written with researchers and advanced, well-trained students in mind. The authors have tried to meet the needs both of students wishing to learn the basics of an important area of research as well as researchers who desire a fairly comprehensive reference for the theory and applications of $\textrm{C}*$-approximation theory.

Author: Gert Kjaergård Pedersen
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 448

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Author:
Publisher:
ISBN:
Category : Securities
Languages : en
Pages : 264

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Author: Elias G. Katsoulis
Publisher: American Mathematical Soc.
ISBN: 1470435454
Category : Mathematics
Languages : en
Pages : 100

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Book Description
The authors study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. They develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to our context. They complement their generic results with the detailed study of many important special cases. In particular they study crossed products of tensor algebras, triangular AF algebras and various associated C -algebras. They make contributions to the study of C -envelopes, semisimplicity, the semi-Dirichlet property, Takai duality and the Hao-Ng isomorphism problem. They also answer questions from the pertinent literature.