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Item Details
| Title:
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COMPLEX INTERPOLATION BETWEEN HILBERT, BANACH AND OPERATOR SPACES
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| By: |
Gilles Pisier |
| Format: |
Paperback |
| List price:
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£64.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821848429 |
| ISBN 13: |
9780821848425 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 November, 2010 |
| Series: |
Memoirs of the American Mathematical Society |
| Pages: |
78 |
| Description: |
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). |
| 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). |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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