Factorization of Linear Operators and Geometry of Banach Spaces: Regional Conference - Brossura

Pisier, Gilles

Brossura

ISBN 10: 0821807102 ISBN 13: 9780821807101

Casa editrice: Amer Mathematical Society, 1986

Riassunto

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.

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Product Description

Book by Gilles Pisier

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 1986
• Lingua: Inglese
• ISBN 10: 0821807102
• ISBN 13: 9780821807101
• Rilegatura: Copertina flessibile
• Numero di pagine: 154
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile