Author: Raymond A. Ryan
Publisher: Springer Science & Business Media
ISBN: 1447139038
Category : Mathematics
Languages : en
Pages : 229
Book Description
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
Author: Raymond A. Ryan
Publisher: Springer Science & Business Media
ISBN: 1447139038
Category : Mathematics
Languages : en
Pages : 229
Book Description
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.
Publisher: Springer Science & Business Media
ISBN: 1447139038
Category : Mathematics
Languages : en
Pages : 229
Book Description
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.
Approximation Theory in Tensor Product Spaces
Author: William A. Light
Publisher: Springer
ISBN: 3540397418
Category : Mathematics
Languages : en
Pages : 164
Book Description
Publisher: Springer
ISBN: 3540397418
Category : Mathematics
Languages : en
Pages : 164
Book Description
Lecture Notes in Mathematics
Author:
Publisher:
ISBN: 9780387087641
Category : Banach spaces
Languages : en
Pages : 99
Book Description
Publisher:
ISBN: 9780387087641
Category : Banach spaces
Languages : en
Pages : 99
Book Description
Tensor Products of C*-Algebras and Operator Spaces
Author: Gilles Pisier
Publisher: Cambridge University Press
ISBN: 1108786472
Category : Mathematics
Languages : en
Pages : 495
Book Description
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.
Publisher: Cambridge University Press
ISBN: 1108786472
Category : Mathematics
Languages : en
Pages : 495
Book Description
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.
Functors and Categories of Banach Spaces
Author: P.W. Michor
Publisher: Springer
ISBN: 3540358471
Category : Mathematics
Languages : en
Pages : 104
Book Description
Publisher: Springer
ISBN: 3540358471
Category : Mathematics
Languages : en
Pages : 104
Book Description
Bilinear Maps and Tensor Products in Operator Theory
Author: Carlos S. Kubrusly
Publisher:
ISBN: 9783031340949
Category :
Languages : en
Pages : 0
Book Description
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.
Publisher:
ISBN: 9783031340949
Category :
Languages : en
Pages : 0
Book Description
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.
Schwartz Spaces, Nuclear Spaces and Tensor Products
Author: Y.-C. Wong
Publisher: Springer
ISBN: 3540351612
Category : Mathematics
Languages : en
Pages : 426
Book Description
Publisher: Springer
ISBN: 3540351612
Category : Mathematics
Languages : en
Pages : 426
Book Description
Tensor Products of Banach Spaces with Unconditional Bases
Tensor Products of C*-algebras and Operator Spaces
Author: Gilles Pisier
Publisher: Cambridge University Press
ISBN: 1108479014
Category : Mathematics
Languages : en
Pages : 495
Book Description
Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.
Publisher: Cambridge University Press
ISBN: 1108479014
Category : Mathematics
Languages : en
Pages : 495
Book Description
Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.
Tensor Products of C*-algebras
Author: Alain Guichardet
Publisher:
ISBN:
Category : C*-algebras
Languages : en
Pages : 204
Book Description
Publisher:
ISBN:
Category : C*-algebras
Languages : en
Pages : 204
Book Description