Introduction To Tensor Products Of Banach Spaces
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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.
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.
Introduction To Tensor Products Of Banach Spaces
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Author : Raymond A. Ryan
language : en
Publisher:
Release Date : 2014-01-15
Introduction To Tensor Products Of Banach Spaces written by Raymond A. Ryan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Approximation Theory In Tensor Product Spaces
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Author : William A. Light
language : en
Publisher: Springer
Release Date : 2006-11-14
Approximation Theory In Tensor Product Spaces written by William A. Light and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Functors And Categories Of Banach Spaces
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Author : P.W. Michor
language : en
Publisher: Springer
Release Date : 2006-11-15
Functors And Categories Of Banach Spaces written by P.W. Michor and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Tensor Spaces And Numerical Tensor Calculus
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Author : Wolfgang Hackbusch
language : en
Publisher: Springer Nature
Release Date : 2019-12-16
Tensor Spaces And Numerical Tensor Calculus written by Wolfgang Hackbusch and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-16 with Mathematics categories.
Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.
Fredholm Theory In Banach Spaces
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Author : Anthony Francis Ruston
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-03
Fredholm Theory In Banach Spaces written by Anthony Francis Ruston 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 2004-06-03 with Mathematics categories.
Presents analogues for operators on Banach spaces of Fredholm's solution of integral equations of the second kind.
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.
Manifolds Tensor Analysis And Applications
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Author : Ralph Abraham
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Manifolds Tensor Analysis And Applications written by Ralph Abraham 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 2012-12-06 with Mathematics categories.
The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.
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.