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OverviewThis 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 DetailsAuthor: Gilles PisierPublisher: American Mathematical Society Imprint: American Mathematical Society Edition: UK ed. Volume: No. 60 Dimensions: Width: 17.70cm , Height: 1.00cm , Length: 25.10cm Weight: 0.316kg ISBN: 9780821807101ISBN 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."ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |