Introduction to Tensor Products of Banach Spaces

Book Description

This volume provides a self-contained introduction to the theory of tensor products of Banach spaces. It is written for graduate students in analysis or for researchers in other fields who wish to become acquainted with this area. The only prerequisites are a basic knowledge of functional analysis and measure theory.Features of particular interest include:- A full treatment of the Grothendieck theory of tensor norms;- Coverage of the Chevet-Saphar norms and their duals, along with the associated classes of nuclear, integral and summing operators;- Chapters on the approximation property and the Radon-Nikodym property;- Topics such as the Bochner and Pettis integrals, the principle of local reflexivity and the Grothendieck inequality placed in a natural setting;- The classes of operators generated by a tensor norm and connections with the theory of operator ideals.Each chapter is accompanied by worked examples and a set of exercises, and two appendices provide essential material on summability in Banach spaces and properties of spaces of measures that may be new to the beginner.

Customer Reviews:

Excelent book........2007-01-10

I'm new studying tensor products, but I found this book clearly written and with clean notational use.

FITHIS reads.......2004-03-10

Dr Ryan gave a draft of the first chapter to my supervisor Dr Sarantopoulos . He also gave me Ryan's thesis . I was fascinated because I knew only the algebraic side of the subject . The first chapter introduced me to a some aspects of functional analysis like Rademacher techniques and nuclear operators . When the book was released I hesitated to give the money . However I thought that the rest chapters would be as great . AND this TRUE . I recommend this book to everyone wanting to learn on topological tensor products ( OK , OK , Banach space tensor products) since this understanding is essential for Banach algebras and factorization in Banach spaces . I believe in retrospect that the money are not that much for the content provided . I hope Dr Ryan will publish his thesis also . To point out how good is this book I urge you to read Barry Johnsons Cohomology of Banach algebras , both give a very good picture . Also Beuazamy's book (Operator Theory) has a proof on the dulality between N(H) and B(H) . Ryans book is essential for the explanation of this phenomenon .

Introduction to Subfactors (London Mathematical Society Lecture Note Series)

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Introduction to Subfactors (London Mathematical Society Lecture Note Series)
V. Jones , and V. S. Sunder
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521584205

Book Description

Subfactors, a subject of considerable research activity for about fifteen years, are known to have significant relations with other fields such as low dimensional topology and algebraic quantum field theory. The authors present a new pictorial approach to subfactors in addition to discussions of basic principles. This book provides an important introduction to the subject and is aimed at students with only a little familiarity with the theory of Hilbert space and other newcomers to the field.

Banach Algebra Techniques in Operator Theory (Graduate Texts in Mathematics)

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Disappointing

Banach Algebra Techniques in Operator Theory (Graduate Texts in Mathematics)
Ronald G. Douglas
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387983775

Book Description

Operator theory is a diverse area of mathematics which derives its impetus and motivation from several sources. It began with the study of integral equations and now includes the study of operators and collections of operators arising in various branches of physics and mechanics. The intention of this book is to discuss certain advanced topics in operator theory and to provide the necessary background for them assuming only the standard senior-first year graduate courses in general topology, measure theory, and algebra. At the end of each chapter there are source notes which suggest additional reading along with giving some comments on who proved what and when. In addition, following each chapter is a large number of problems of varying difficulty. This new edition will appeal to a new generation of students seeking an introduction to operator theory.

Customer Reviews:

Disappointing.......2001-02-23

If this book is disappointing why did I rate it 5 stars? Well, it is because having studied the first edition I was expecting more updates in the second. It really is an excellent book, but I wanted the author to discuss the Brown-Douglas-Fillmore K-theory of operator algebras and give an in-depth discussion of the invariant subspace conjecture. I used this book for a two semester course in functional analysis and operator theory while a sophomore in undergraduate and found it very challenging. The presentation of the topics is very quick and the problems are pretty difficult, but you take away an appreciation of this important area of mathematics. Indeed, the theory of Hp-spaces and Toeplitz operators, which are covered in the last two chapters, have many applications in engineering and physics. The author does give an update on the problems he marked with two stars (indicating an unsolved problem) in the first edition, and references that discuss their solution. When studying the book, I am always amazed about how rich linear transformations become when they operate on infinite-dimensional Hilbert spaces; but also how much the finite-dimensional results have generalizations in infinite dimensions. The theory of C* and W*-algebras is discussed in the book, and the presentation should be helpful to physicists who use these techniques, even though the presentation is much more general than one would find in physical theories. The explanation of the W*-algebra as arising from the enlargement of the functional calculus to an algebra of functions generated by characteristic functions; where the Gelfand transform is taken on a larger commutative self-adjoint subalgebra of the space of linear operators is one that is easier to remember and seems more natural than merely giving a set of axioms that a W*-algebra is supposed to satisfy. A very abstract discussion of index theory is given, and one that is pretty distant from the theory of integral equations, but with some work one can see the connection to these equations. Who knows, maybe a third edition with more of the author's insights?

Handbook of the Geometry of Banach Spaces : Volume 1

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Handbook of the Geometry of Banach Spaces : Volume 1

Manufacturer: North Holland
ProductGroup: Book
Binding: Hardcover

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ASIN: 0444828427

Book Description

The Handbook presents an overview of most aspects of modern
Banach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations.

The Handbook begins with a chapter on basic concepts in Banach
space theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers.

Book Description

Almost Automorphic and Almost Periodic Functions in Abstract Spaces introduces and develops the theory of almost automorphic vector-valued functions in Bochner's sense and the study of almost periodic functions in a locally convex space in a homogenous and unified manner. It also applies the results obtained to study almost automorphic solutions of abstract differential equations, expanding the core topics with a plethora of groundbreaking new results and applications. For the sake of clarity, and to spare the reader unnecessary technical hurdles, the concepts are studied using classical methods of functional analysis.

Almost Periodic Solutions of Differential Equations in Banach Spaces

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Almost Periodic Solutions of Differential Equations in Banach Spaces
Yoshiyuki Hino
Manufacturer: Taylor & Francis
ProductGroup: Book
Binding: Hardcover

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Book Description

The authors present recent developments in spectral conditions for the existence of periodic and almost periodic solutions of inhomogenous equations in Banach Spaces. Many of the results represent significant advances in this area. In particular, a new approach based on the so-called evolution semigroups with an original decomposition technique is systematically presented. The monograph also includes extensions of classical methods, such as fixed points and stability methods, to abstract functional differential equations with applications to partial functional differential equations.

Analytic Hilbert Modules (Chapman & Hall/Crc Research Notes in Mathematics Series.)

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Analytic Hilbert Modules (Chapman & Hall/Crc Research Notes in Mathematics Series.)
Xiaoman Chen , and Kunyu Guo
Manufacturer: Chapman & Hall/CRC
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Binding: Hardcover

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Book Description

The seminal 1989 work of Douglas and Paulsen on the theory of Hilbert modules over function algebras precipitated a number of major research efforts. This in turn led to some intriguing and valuable results, particularly in the areas of operator theory and functional analysis. With the field now beginning to blossom, the time has come to collect those results in one volume. Written by two of the most active and often-cited researchers in the field, Analytic Hilbert Modules offers a clear, logical survey of recent developments, including advances made by authors and others. It provides much-needed insight into function theory of several variables and includes significant results published here for the first time in areas such as characteristic space theory, rigidity phenomena, the equivalence problem, Arveson modules, extension theory, and reproducing Hilbert spaces on n-dimensional complex space.

Atomic Boolean Subspace Lattices and Applications to the Theory of Bases (Memoirs of the American Mathematical Society)

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Atomic Boolean Subspace Lattices and Applications to the Theory of Bases (Memoirs of the American Mathematical Society)
S. Argyros , M. Lambrou , and W. E. Longstaff
Manufacturer: Amer Mathematical Society
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Binding: Paperback

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Banach Algebras '97: Proceedings of the 13th International Conference on Banach Algebras Held at the Heinrich Fabri Institute of the University of Tubingen in Blaubeuren,

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Banach Algebras '97: Proceedings of the 13th International Conference on Banach Algebras Held at the Heinrich Fabri Institute of the University of Tubingen in Blaubeuren,

Manufacturer: Walter de Gruyter
ProductGroup: Book
Binding: Hardcover

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Banach Space Theory and Its Applications (Lecture Notes in Mathematics)

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Banach Space Theory and Its Applications (Lecture Notes in Mathematics)

Manufacturer: Springer-Verlag
ProductGroup: Book
Binding: Paperback

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Customer Reviews:

CHUCKLES ABOUND IN THE RUMINATIONS OF STOUT MAMA.......2006-04-14

Remember Stout Mama, the fresh, funny doyenne who comments on ordinary events in an extraordinary way? Well, it took me a while but I just discovered she's out in paperback, and it's just as much fun the second time around.

Just listen to how Stout feels about dieting: "Stout Mama doesn't understand the science of weight loss. Gaining is easy. The food comes to visit and, like poor relations stays. Doritos in her thighs, the round blush of chocolate-covered cherries in her cheeks."

Stout Mama knows how to relate to every female extant, whether through her views on travel, love, life or being "with it". She's the kind of witty and wise friend you wish lived next door.

All who want a good chuckle will find them by the hundreds in the ruminations of Stout Mama.

- Gail Cooke

STOUT MAMA IS FULL BODIED READING PLEASURE!.......1999-12-29

This book is proof good things come in small packages. Each short story (and some are only a page long) is chock full of vivid visual imagery, decisively descriptive language, and multi-layered meaning. Stout Mama is in her pre "When I Am Old, I Will Wear Purple" stage, but you know she'll be sporting loud lavenders later on. She's the kind of woman we'd like to emulate or evolve into, and Ms. James has the kind of adjectival accuracy we all envy. Cherish this woman and this book.

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The Adventures of Stout Mama
Sibyl JAmes
Manufacturer: New York Papier-MAche 1992.
ProductGroup: Book
Binding: Hardcover
ASIN: B000N1AONO

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The Adventures of Stout Mama
Sibyl James
Manufacturer: Watsonville, CA: Papier-Mache Press, 1993
ProductGroup: Book
Binding: Hardcover
ASIN: B000NVNUPS

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The Adventures of Stout Mama
Sibyl James
Manufacturer: Papier Mache Pr
ProductGroup: Book
Binding: Hardcover
ASIN: B000NUFKBQ

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The ADVENTURES Of STOUT MAMA.
Sibyl. James
Manufacturer: Papier-Mache Press,
ProductGroup: Book
Binding: Hardcover
ASIN: B000NYAY2C

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