The Metric Theory of Tensor Products: Grothendieck's Resume Revisited

The Metric Theory of Tensor Products: Grothendieck's Resume Revisited

By: Jan H. Fourie (author), Johan Swart (author), Joe Diestel (author)Hardback

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Description

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.

Contents

Basics on tensor norms The role of $C(K)$-spaces and $L^1$-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.

Product Details

  • ISBN13: 9780821844403
  • Format: Hardback
  • Number Of Pages: 287
  • ID: 9780821844403
  • ISBN10: 0821844407

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