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# The metric theory of tensor products : Grothendieck's résumé revisited

Autor: Joseph Diestel; A Grothendieck; Jan H Fourie; J Swart Providence, R.I. : American Mathematical Society, ©2008. Libro : Inglés (eng)Ver todas las ediciones y todos los formatos "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 JACKET.  Leer más (todavía no calificado) 0 con reseñas - Ser el primero.

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## Detalles

Tipo de material: Recurso en Internet Libro/Texto, Recurso en Internet Joseph Diestel; A Grothendieck; Jan H Fourie; J Swart Encontrar más información sobre: Joseph Diestel A Grothendieck Jan H Fourie J Swart 9780821844403 0821844407 185095773 x, 278 p. : ill. ; 27 cm. Basics on tensor norms; The role of $C(K)$-spaces and $L1$-spaces; $\otimes$-norms related to Hilbert space; The fundamental theorem and its consequences; Glossary of terms; The problems of the Resume; The Blaschke selection principle and compact convex sets in finite dimensional Banach spaces; A short introduction to Banach lattices; Stonean spaces and injectivity; Epilogue; Bibliography; Author index; Index of notation; Index. Joe Diestel, Jan H. Fourie, Johan Swart.

### Resumen:

"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 JACKET.

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