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The Metric Theory of Tensor Products: Grothendieck's Résumé Revisited
Joe Diestel, Kent State University, OH, Jan H. Fourie, North-West University, Potchefstroom, South Africa, and Johan Swart, University of Pretoria, South Africa

2008; 278 pp; hardcover
ISBN-10: 0-8218-4440-7
ISBN-13: 978-0-8218-4440-3
List Price: US$86
Member Price: US$68.80
Order Code: MBK/52
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Grothendieck's Resumé 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.


Graduate students and research mathematicians interested in abstract analysis, Banach space theory, functional analysis, and operator theory.


"(The book) scores on several counts, not just as a serious scholarly contribution to functional analysis, but as a tribute to Grothendiecks incomparable gifts in the area of innovation and originality."

-- MAA Reviews

"The exposition is clear, well-motivated and reasonably self-contained."

-- Mathematical Reviews

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