The Metric Theory of Tensor Products

by Diestel, Joe; Fourie, Jan H.; Swart, Johan

• ISBN13: 9780821844403
• ISBN10: 0821844407
• Format: Hardcover
• Copyright: 2008-06-12
• Publisher: Amer Mathematical Society

Summary

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 ofoperators 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.

Table of 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

Table of Contents provided by Publisher. All Rights Reserved.