Complex interpolation between Hilbert, Banach and operator spaces
Author(s)
Bibliographic Information
Complex interpolation between Hilbert, Banach and operator spaces
（Memoirs of the American Mathematical Society, no. 978）
American Mathematical Society, c2010
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Note
"Volume 208, number 978 (third of 6 numbers)."
Includes bibliographical references (p. 75-78)
Description and Table of Contents
Description
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).
by "Nielsen BookData"