Complex interpolation between Hilbert, Banach and operator spaces. Memoirs of the American Mathematical Society; 978 = Vol. 208, Nr. 3.

Pisier, Gilles

ISBN 10: 0821848429 / ISBN 13: 9780821848425

Edité par Providence, American Math. Soc, 2010

A propos de cet article

Ex-library in GOOD condition with library-signature and stamp(s). Some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-00343 9780821848425 Sprache: Englisch Gewicht in Gramm: 150.

N° de réf. du vendeur 2482853

Détails bibliographiques

• Titre: Complex interpolation between Hilbert, Banach and operator spaces. Memoirs of the American Mathematical Society; 978 = Vol. 208, Nr. 3.
• Éditeur: Providence, American Math. Soc
• Date de parution: 2010
• Langue: anglais
• ISBN à 10 chiffres: 0821848429
• ISBN à 13 chiffres: 9780821848425
• Reliure: Softcover
• Catalogues du vendeur:
  • SA MATHEMATIK

A propos de ce titre

Synopsis

Motivated by a question of Vincent Lafforgue, the author studies the Banach spaces X satisfying the following property: there is a function \varepsilon\to \Delta_X(\varepsilon) tending to zero with \varepsilon>0 such that every operator T\colon \ L_2\to L_2 with \|T\|\le \varepsilon that is simultaneously contractive (i.e., of norm \le 1) on L_1 and on L_\infty must be of norm \le \Delta_X(\varepsilon) on L_2(X). The author shows that \Delta_X(\varepsilon) \in O(\varepsilon^\alpha) for some \alpha>0 if X is isomorphic to a quotient of a subspace of an ultraproduct of \theta-Hilbertian spaces for some \theta>0 (see Corollary 6.7), where \theta-Hilbertian is meant in a slightly more general sense than in the author's earlier paper (1979).