Tensor Norms And Operator Ideals

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Tensor Norms And Operator Ideals

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Author : A. Defant
language : en
Publisher: Elsevier
Release Date : 1992-11-26

Tensor Norms And Operator Ideals written by A. Defant and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-11-26 with Mathematics categories.

The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exercises.

Introduction To Tensor Products Of Banach Spaces

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Author : Raymond A. Ryan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Introduction To Tensor Products Of Banach Spaces written by Raymond A. Ryan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

This book is intended as an introduction to the theory of tensor products of Banach spaces. The prerequisites for reading the book are a first course in Functional Analysis and in Measure Theory, as far as the Radon-Nikodym theorem. The book is entirely self-contained and two appendices give addi tional material on Banach Spaces and Measure Theory that may be unfamil iar to the beginner. No knowledge of tensor products is assumed. Our viewpoint is that tensor products are a natural and productive way to understand many of the themes of modern Banach space theory and that "tensorial thinking" yields insights into many otherwise mysterious phenom ena. We hope to convince the reader of the validity of this belief. We begin in Chapter 1 with a treatment of the purely algebraic theory of tensor products of vector spaces. We emphasize the use of the tensor product as a linearizing tool and we explain the use of tensor products in the duality theory of spaces of operators in finite dimensions. The ideas developed here, though simple, are fundamental for the rest of the book.

Upper Bounds For Grothendieck Constants Quantum Correlation Matrices And Ccp Functions

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Author : Frank Oertel
language : en
Publisher: Springer Nature
Release Date : 2024-09-12

Upper Bounds For Grothendieck Constants Quantum Correlation Matrices And Ccp Functions written by Frank Oertel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-12 with Mathematics categories.

This book concentrates on the famous Grothendieck inequality and the continued search for the still unknown best possible value of the real and complex Grothendieck constant (an open problem since 1953). It describes in detail the state of the art in research on this fundamental inequality, including Krivine's recent contributions, and sheds light on related questions in mathematics, physics and computer science, particularly with respect to the foundations of quantum theory and quantum information theory. Unifying the real and complex cases as much as possible, the monograph introduces the reader to a rich collection of results in functional analysis and probability. In particular, it includes a detailed, self-contained analysis of the multivariate distribution of complex Gaussian random vectors. The notion of Completely Correlation Preserving (CCP) functions plays a particularly important role in the exposition. The prerequisites are a basic knowledge of standard functional analysis, complex analysis, probability, optimisation and some number theory and combinatorics. However, readers missing some background will be able to consult the generous bibliography, which contains numerous references to useful textbooks. The book will be of interest to PhD students and researchers in functional analysis, complex analysis, probability, optimisation, number theory and combinatorics, in physics (particularly in relation to the foundations of quantum mechanics) and in computer science (quantum information and complexity theory).

History Of Banach Spaces And Linear Operators

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Author : Albrecht Pietsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-31

History Of Banach Spaces And Linear Operators written by Albrecht Pietsch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-31 with Mathematics categories.

Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.

Recent Advances In Operator Theory Operator Algebras And Their Applications

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Author : Dumitru Gaspar
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30

Recent Advances In Operator Theory Operator Algebras And Their Applications written by Dumitru Gaspar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Mathematics categories.

This book offers peer-reviewed articles from the 19th International Conference on Operator Theory, Summer 2002. It contains recent developments in a broad range of topics from operator theory, operator algebras and their applications, particularly to differential analysis, complex functions, ergodic theory, mathematical physics, matrix analysis, and systems theory. The book covers a large variety of topics including single operator theory, C*-algebras, diffrential operators, integral transforms, stochastic processes and operators, and more.

Descriptive Topology And Functional Analysis Ii

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Author : Juan Carlos Ferrando
language : en
Publisher: Springer
Release Date : 2019-06-02

Descriptive Topology And Functional Analysis Ii written by Juan Carlos Ferrando and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-02 with Mathematics categories.

This book is the result of a meeting on Topology and Functional Analysis, and is dedicated to Professor Manuel López-Pellicer's mathematical research. Covering topics in descriptive topology and functional analysis, including topological groups and Banach space theory, fuzzy topology, differentiability and renorming, tensor products of Banach spaces and aspects of Cp-theory, this volume is particularly useful to young researchers wanting to learn about the latest developments in these areas.

Orthonormal Systems And Banach Space Geometry

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Author : Albrecht Pietsch
language : en
Publisher: Cambridge University Press
Release Date : 1998-09-10

Orthonormal Systems And Banach Space Geometry written by Albrecht Pietsch and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-10 with Mathematics categories.

This book describes the interplay between orthonormal expansions and Banach space geometry.

Advanced Courses Of Mathematical Analysis Ii

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Author : A. Rodriguez-Palacios
language : en
Publisher: World Scientific
Release Date : 2007

Advanced Courses Of Mathematical Analysis Ii written by A. Rodriguez-Palacios and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

This volume comprises a collection of articles by leading researchers in mathematical analysis. It provides the reader with an extensive overview of new directions and advances in topics for current and future research in the field.

Methods In Banach Space Theory

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Author : Jesus M. F. Castillo
language : en
Publisher: Cambridge University Press
Release Date : 2006-11-30

Methods In Banach Space Theory written by Jesus M. F. Castillo and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-30 with Mathematics categories.

A comprehensive overview of modern Banach space theory.

Recent Progress In Functional Analysis

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Author : K.D. Bierstedt
language : en
Publisher: Elsevier
Release Date : 2001-09-20

Recent Progress In Functional Analysis written by K.D. Bierstedt and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-09-20 with Mathematics categories.

This Proceedings Volume contains 32 articles on various interesting areas ofpresent-day functional analysis and its applications: Banach spaces andtheir geometry, operator ideals, Banach and operator algebras, operator andspectral theory, Frechet spaces and algebras, function and sequence spaces.The authors have taken much care with their articles and many papers presentimportant results and methods in active fields of research. Several surveytype articles (at the beginning and the end of the book) will be very usefulfor mathematicians who want to learn "what is going on" in some particularfield of research.