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Introduction To Tensor Products Of Banach Spaces
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Book Synopsis Introduction to Tensor Products of Banach Spaces by : Raymond A. Ryan
Download or read book Introduction to Tensor Products of Banach Spaces written by Raymond A. Ryan and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Approximation Theory in Tensor Product Spaces by : William A. Light
Download or read book Approximation Theory in Tensor Product Spaces written by William A. Light and published by Springer. This book was released on 2006-11-14 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lecture Notes in Mathematics written by and published by . This book was released on 1964 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Tensor Products of C*-Algebras and Operator Spaces by : Gilles Pisier
Download or read book Tensor Products of C*-Algebras and Operator Spaces written by Gilles Pisier and published by Cambridge University Press. This book was released on 2020-02-27 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the author's university lecture courses, this book presents the many facets of one of the most important open problems in operator algebra theory. Central to this book is the proof of the equivalence of the various forms of the problem, including forms involving C*-algebra tensor products and free groups, ultraproducts of von Neumann algebras, and quantum information theory. The reader is guided through a number of results (some of them previously unpublished) revolving around tensor products of C*-algebras and operator spaces, which are reminiscent of Grothendieck's famous Banach space theory work. The detailed style of the book and the inclusion of background information make it easily accessible for beginning researchers, Ph.D. students, and non-specialists alike.
Book Synopsis Functors and Categories of Banach Spaces by : P.W. Michor
Download or read book Functors and Categories of Banach Spaces written by P.W. Michor and published by Springer. This book was released on 2006-11-15 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Schwartz Spaces, Nuclear Spaces and Tensor Products by : Y.-C. Wong
Download or read book Schwartz Spaces, Nuclear Spaces and Tensor Products written by Y.-C. Wong and published by Springer. This book was released on 2006-11-15 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Tensor Products of Banach Spaces with Unconditional Bases by : Martin Strauch
Download or read book Tensor Products of Banach Spaces with Unconditional Bases written by Martin Strauch and published by . This book was released on 1985 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Semi-tensor Product of Matrices and Its Applications by : Dai-Zhan Cheng
Download or read book An Introduction to Semi-tensor Product of Matrices and Its Applications written by Dai-Zhan Cheng and published by World Scientific. This book was released on 2012 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: A generalization of Conventional Matrix Product (CMP), called the Semi-Tensor Product (STP), is proposed. It extends the CMP to two arbitrary matrices and maintains all fundamental properties of CMP. In addition, it has a pseudo-commutative property, which makes it more superior to CMP. The STP was proposed by the authors to deal with higher-dimensional data as well as multilinear mappings. After over a decade of development, STP has been proven to be a powerful tool in dealing with nonlinear and logical calculations.This book is a comprehensive introduction to the theory of STP and its various applications, including logical function, fuzzy control, Boolean networks, analysis and control of nonlinear systems, amongst others.
Book Synopsis Tensor Products of C*-algebras and Operator Spaces by : Gilles Pisier
Download or read book Tensor Products of C*-algebras and Operator Spaces written by Gilles Pisier and published by Cambridge University Press. This book was released on 2020-02-27 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.
Book Synopsis Tensor Products of C*-algebras by : Alain Guichardet
Download or read book Tensor Products of C*-algebras written by Alain Guichardet and published by . This book was released on 1969 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bilinear Maps and Tensor Products in Operator Theory by : Carlos S. Kubrusly
Download or read book Bilinear Maps and Tensor Products in Operator Theory written by Carlos S. Kubrusly and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Banach Space Theory by : Marián Fabian
Download or read book Banach Space Theory written by Marián Fabian and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.
Book Synopsis The Metric Theory of Tensor Products by : Joseph Diestel
Download or read book The Metric Theory of Tensor Products written by Joseph Diestel and published by Amer Mathematical Society. This book was released on 2008 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Metric Theory of Tensor Products by : Joseph Diestel
Download or read book The Metric Theory of Tensor Products written by Joseph Diestel and published by American Mathematical Soc.. This book was released on 2008-01-01 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Positivity written by Karim Boulabiar and published by Springer Science & Business Media. This book was released on 2007-12-16 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents nine survey articles addressing topics surrounding positivity, with an emphasis on functional analysis. The book assembles a wide spectrum of research into positivity, providing up-to-date information on topics of current interest. The discussion provides insight into classical areas like spaces of continuous functions, f-algebras, and integral operators. The coverage extends is broad, including vector measures, operator spaces, ordered tensor products, and non-commutative Banach function spaces.
Book Synopsis Trends in Banach Spaces and Operator Theory by : Anna Kamińska
Download or read book Trends in Banach Spaces and Operator Theory written by Anna Kamińska and published by American Mathematical Soc.. This book was released on 2003 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Operator Space Theory by : Gilles Pisier
Download or read book Introduction to Operator Space Theory written by Gilles Pisier and published by Cambridge University Press. This book was released on 2003-08-25 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the theory of operator spaces, emphasising applications to C*-algebras.
