Introduction to Tensor Products of Banach Spaces 2002nd Edition by Raymond A. Ryan (PDF)

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.

User’s Reviews

Editorial Reviews: Review From the reviews:”The book under review is intended to serve as an introduction to the theory of tensor products of Banach spaces. … it is a most welcome addition to the existing literature and appears to be well-suited as a guide and as a textbook in lectures, seminars, etc., for students … . Each chapter is accompanied by a set of exercises. … The book is very carefully written and edited. The text makes very good reading … .” (Hans Jarchow, Zentralblatt MATH, Vol. 1090 (16), 2006)”This book provides a self-contained introduction to tensor products of Banach spaces. … Each chapter is accompanied by exercises with illustrate mathematical concepts and propositions introduced there. The more or less straightforward solution of most of these exercises leads the reader to a better understanding of the material. … It is accessible, clearly organized, and well written. It can be highly recommended to graduate students and mathematicians interested in functional analysis.” (K. –D Kürsten, Zeitschrift für Analysis und ihre Anwendungen, Vol. 24 (4), 2005)”The author sets out to give an accessible account of some chosen topics from the theory of tensor products for Banach spaces … . The result is a very well written, beautiful book … presenting a coherent, originally arranged and presented overview of various classical results. The book is self-contained and presented in a way that it at the same time is an accessible text for graduate students, as well as a very good basic reference for researchers … .” (Mark Sioen, Simon Stevin Bulletin, Vol. 11 (2), 2004)”This book is a good source to learn the basic notions of tensor products … . The book can be recommended to everybody who is interested in the theory of tensor products and their applications, but first of all, to beginners in this field.” (Endre Durszt, Acta Scientiarum Mathematicarum, Vol. 69, 2003)”This book provides a self-contained introduction to the theory of tensor products on Banach spaces. Being the first book with a clear focus not only on graduate students in analysis, but also researchers who wish to become acquainted with the elementary facts of this area, it is a welcome addition to the literature. … The book contains a large number of interesting exercises.” (Andreas Defant, Mathematical Reviews, Issue 2003 f)”The aim of the present book is to give a thorough and relatively short introduction to tensor products of Banach spaces … and bringing the reader to the frontier of current research in the area. … The book is an excellent introduction to the theory of tensor products and it is highly recommended to graduate students in analysis and to researchers in other areas needing results from this field.” (S. Cobzas, Studia Universitatis Babes-Bolyai, Vol. XLVII (4), 2002)

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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 .

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Introduction to Tensor Products of Banach Spaces 2002nd Edition 2002 PDF Free Download
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