Overview

This book surveys the considerable progress made in Banach space theory as a result of Grothendieck's fundamental paper Resume de la theorie metrique des produits tensoriels topologiques. The author examines the central question of which Banach spaces X and Y have the property that every bounded operator from X to Y factors through a Hilbert space. He reviews the six problems posed at the end of Grothendieck's paper, which have now all been solved (except perhaps the exact value of Grothendieck's constant), and includes the various results which led to their solution. The last chapter contains the author's construction of several Banach spaces such that the injective and projective tensor products coincide; this gives a negative solution to Grothendieck's sixth problem.

Full Product Details

Author:   Gilles Pisier
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Edition:   UK ed.
Volume:   No. 60
Weight:   0.316kg
ISBN:  

9780821807101

ISBN 10:   0821807102
Pages:   154
Publication Date:   30 December 1986
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   Temporarily unavailable  
The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you.

Table of Contents

"Absolutely summing operators and basic applications Factorization through a Hilbert space Type and cotype. Kwapien's theorem The """"abstract"""" version of Grothendieck's theorem Grothendieck's theorem Banach spaces satisfying Grothendieck's theorem Applications of the volume ratio method Banach lattices $C^*$-algebras Counterexamples to Grothendieck's conjecture."

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions