Pisier:Factor Linear Oper Cbms 60 P Expanded Lectures
Regional Conference
Gilles Pisier(Author)
American Mathematical Society (Publisher)
Will be published approx. on 30. December 1986
Book
Paperback/Softback
154 pages
978-0-8218-0710-1 (ISBN)
Description
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, in particular when the operators are defined on a Banach lattice, a $C^*$-algebra or the disc algebra and $H^\infty$. 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.Although the book is aimed at mathematicians working in functional analysis, harmonic analysis and operator algebras, its detailed and self-contained treatment makes the material accessible to nonspecialists with a grounding in basic functional analysis. In fact, the author is particularly concerned to develop very recent results in the geometry of Banach spaces in a form that emphasizes how they may be applied in other fields, such as harmonic analysis and $C^*$-algebras.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
College/higher education
Professional and scholarly
Dimensions
Height: 251 mm
Width: 177 mm
Thickness: 10 mm
Weight
316 gr
ISBN-13
978-0-8218-0710-1 (9780821807101)
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Schweitzer Classification
Content
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.