On the connection between real and complex interpolation of quasi-banach spaces
نویسندگان
چکیده
منابع مشابه
Interpolation of bilinear operators between quasi-Banach spaces
We study interpolation, generated by an abstract method of means, of bilinear operators between quasi-Banach spaces. It is shown that under suitable conditions on the type of these spaces and the boundedness of the classical convolution operator between the corresponding quasi-Banach sequence spaces, bilinear interpolation is possible. Applications to the classical real method spaces, Calderón-...
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Motivated by a question of Vincent Lafforgue, we study the Banach spaces X satisfying the following property: there is a function ε → ∆ X (ε) tending to zero with ε > 0 such that every operator T : L 2 → L 2 with T ≤ ε that is simultaneously contractive (i.e. of norm ≤ 1) on L 1 and on L ∞ must be of norm ≤ ∆ X (ε) on L 2 (X). We show that ∆ X (ε) ∈ O(ε α) for some α > 0 iff X is isomorphic to ...
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ژورنال
عنوان ژورنال: Bulletin des Sciences Mathématiques
سال: 1998
ISSN: 0007-4497
DOI: 10.1016/s0007-4497(98)80075-4