Complex interpolation between Hilbert, Banach and operator spaces
著者
書誌事項
Complex interpolation between Hilbert, Banach and operator spaces
(Memoirs of the American Mathematical Society, no. 978)
American Mathematical Society, c2010
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注記
"Volume 208, number 978 (third of 6 numbers)."
Includes bibliographical references (p. 75-78)
内容説明・目次
内容説明
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).
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