Tensor Norms and Operator Ideals
Tensor Norms and Operator Ideals

Author: A. Defant

Publisher: Elsevier

Published: 1992-11-26

Total Pages: 579

ISBN-13: 0080872875

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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
Introduction to Tensor Products of Banach Spaces

Author: Raymond A. Ryan

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 229

ISBN-13: 1447139038

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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.

Tensor Norms and Operator Ideals
Tensor Norms and Operator Ideals

Author: A. Defant

Publisher: North Holland

Published: 1992-11-22

Total Pages: 565

ISBN-13: 9780444890917

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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.

The Metric Theory of Tensor Products
The Metric Theory of Tensor Products

Author: Joseph Diestel

Publisher: American Mathematical Soc.

Published: 2008-01-01

Total Pages: 294

ISBN-13: 9780821872697

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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.

Recent Advances in Operator Theory, Operator Algebras, and their Applications
Recent Advances in Operator Theory, Operator Algebras, and their Applications

Author: Dumitru Gaspar

Publisher: Springer Science & Business Media

Published: 2006-03-30

Total Pages: 351

ISBN-13: 3764373148

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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
Descriptive Topology and Functional Analysis II

Author: Juan Carlos Ferrando

Publisher: Springer

Published: 2019-06-02

Total Pages: 302

ISBN-13: 3030173763

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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.