The Metric Theory Of Tensor Products

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The Metric Theory Of Tensor Products

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Author : Joseph Diestel
language : en
Publisher: American Mathematical Soc.
Release Date : 2008-01-01

The Metric Theory Of Tensor Products written by Joseph Diestel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.

Famed mathematician Alexander Grothendieck, in his Resume, set forth his plan for the study of the finer structure of Banach spaces. He used tensor products as a foundation upon which he built the classes of operators most important to the study of Banach spaces and established the importance of the "local" theory in the study of these operators and the spaces they act upon. When Lintenstrauss and Pelczynski addressed his work at the rebirth of Banach space theory, they shed his Fundamental Inequality in the trappings of operator ideals by shedding the tensorial formulation. The authors of this book, however, feel that there is much of value in Grothendieck's original formulations in the Resume and here endeavor to "expose the Resume" by presenting most of Grothendieck's arguments using the mathematical tools that were available to him at the time.

The Metric Theory Of Tensor Products Grothendieck S R Um Revisited

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Author :
language : en
Publisher:
Release Date : 2002

The Metric Theory Of Tensor Products Grothendieck S R Um Revisited written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.

Navorsingsprogram: Bedryfswiskunde en Informatika = Research Programme: Business Mathematics and Informatics.

The Metric Theory Of Tensor Products

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Author : Joseph Diestel
language : en
Publisher: Amer Mathematical Society
Release Date : 2008

The Metric Theory Of Tensor Products written by Joseph Diestel and has been published by Amer Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

Grothendieck's Resume is a landmark in functional analysis. Despite having appeared more than a half century ago, its techniques and results are still not widely known nor appreciated. This is due, no doubt, to the fact that Grothendieck included practically no proofs, and the presentation is based on the theory of the very abstract notion of tensor products. This book aims at providing the details of Grothendieck's constructions and laying bare how the important classes of operators are a consequence of the abstract operations on tensor norms. Particular attention is paid to how the classical Banach spaces ($C(K)$'s, Hilbert spaces, and the spaces of integrable functions) fit naturally within the mosaic that Grothendieck constructed.

Some Results In The Metric Theory Of Tensor Products

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Author : S. Kaijser
language : en
Publisher:
Release Date : 1973

Some Results In The Metric Theory Of Tensor Products written by S. Kaijser and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with categories.

Introduction To Tensor Products Of Banach Spaces

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Author : Raymond A. Ryan
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-01-15

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 2002-01-15 with Mathematics categories.

This is the first ever truly introductory text to the theory of tensor products of Banach spaces. Coverage includes a full treatment of the Grothendieck theory of tensor norms, approximation property and the Radon-Nikodym Property, Bochner and Pettis integrals. Each chapter contains worked examples and a set of exercises, and two appendices offer material on summability in Banach spaces and properties of spaces of measures.

Bilinear Maps And Tensor Products In Operator Theory

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Author : Carlos S. Kubrusly
language : en
Publisher: Springer Nature
Release Date : 2023-11-14

Bilinear Maps And Tensor Products In Operator Theory written by Carlos S. Kubrusly and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-14 with Mathematics categories.

This text covers a first course in bilinear maps and tensor products intending to bring the reader from the beginning of functional analysis to the frontiers of exploration with tensor products. Tensor products, particularly in infinite-dimensional normed spaces, are heavily based on bilinear maps. The author brings these topics together by using bilinear maps as an auxiliary, yet fundamental, tool for accomplishing a consistent, useful, and straightforward theory of tensor products. The author’s usual clear, friendly, and meticulously prepared exposition presents the material in ways that are designed to make grasping concepts easier and simpler. The approach to the subject is uniquely presented from an operator theoretic view. An introductory course in functional analysis is assumed. In order to keep the prerequisites as modest as possible, there are two introductory chapters, one on linear spaces (Chapter 1) and another on normed spaces (Chapter 5), summarizing the background material required for a thorough understanding. The reader who has worked through this text will be well prepared to approach more advanced texts and additional literature on the subject. The book brings the theory of tensor products on Banach spaces to the edges of Grothendieck's theory, and changes the target towards tensor products of bounded linear operators. Both Hilbert-space and Banach-space operator theory are considered and compared from the point of view of tensor products. This is done from the first principles of functional analysis up to current research topics, with complete and detailed proofs. The first four chapters deal with the algebraic theory of linear spaces, providing various representations of the algebraic tensor product defined in an axiomatic way. Chapters 5 and 6 give the necessary background concerning normed spaces and bounded bilinear mappings. Chapter 7 is devoted to the study of reasonable crossnorms on tensor product spaces, discussing in detail the important extreme realizations of injective and projective tensor products. In Chapter 8 uniform crossnorms are introduced in which the tensor products of operators are bounded; special attention is paid to the finitely generated situation. The concluding Chapter 9 is devoted to the study of the Hilbert space setting and the spectral properties of the tensor products of operators. Each chapter ends with a section containing “Additional Propositions" and suggested readings for further studies.

Trends In Banach Spaces And Operator Theory

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Author : Anna Kamińska
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Trends In Banach Spaces And Operator Theory written by Anna Kamińska and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

This volume contains proceedings of the conference on Trends in Banach Spaces and Operator Theory, which was devoted to recent advances in theories of Banach spaces and linear operators. Included in the volume are 25 papers, some of which are expository, while others present new results. The articles address the following topics: history of the famous James' theorem on reflexivity, projective tensor products, construction of noncommutative $L p$-spaces via interpolation, Banach spaces with abundance of nontrivial operators, Banach spaces with small spaces of operators, convex geometry of Coxeter-invariant polyhedra, uniqueness of unconditional bases in quasi-Banach spaces, dynamics of cohyponormal operators, and Fourier algebras for locally compact groupoids. The book is suitable for graduate students and research mathematicians interested in Banach spaces and operator theory and their applications.

Classical Summation In Commutative And Noncommutative Lp Spaces

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Author : Andreas Defant
language : en
Publisher: Springer
Release Date : 2011-06-21

Classical Summation In Commutative And Noncommutative Lp Spaces written by Andreas Defant and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-21 with Mathematics categories.

The aim of this research is to develop a systematic scheme that makes it possible to transform important parts of the by now classical theory of summation of general orthonormal series into a similar theory for series in noncommutative $L_p$-spaces constructed over a noncommutative measure space (a von Neumann algebra of operators acting on a Hilbert space together with a faithful normal state on this algebra).

Operator Analysis

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Author : Jim Agler
language : en
Publisher: Cambridge University Press
Release Date : 2020-03-26

Operator Analysis written by Jim Agler 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 2020-03-26 with Mathematics categories.

This monograph, aimed at graduate students and researchers, explores the use of Hilbert space methods in function theory. Explaining how operator theory interacts with function theory in one and several variables, the authors journey from an accessible explanation of the techniques to their uses in cutting edge research.

Some Random Series Of Functions

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Author : Jean-Pierre Kahane
language : en
Publisher: Cambridge University Press
Release Date : 1985

Some Random Series Of Functions written by Jean-Pierre Kahane 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 1985 with Mathematics categories.

The subject matter of Some Random Series of Functions is important and has wide application in mathematics, statistics, engineering, and physics.