Complex Interpolation Between Hilbert, Banach and Operator Spaces - Brossura

Pisier, Gilles

Brossura

ISBN 10: 0821848429 ISBN 13: 9780821848425

Casa editrice: Amer Mathematical Society, 2010

Riassunto

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).

Dettagli dell?edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 0821848429
• ISBN 13: 9780821848425
• Rilegatura: Copertina flessibile
• Numero di pagine: 78
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile