Geometric interpolation between Hilbert spaces
نویسندگان
چکیده
منابع مشابه
Interpolation between Hilbert , Banach and Operator spaces
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 ...
متن کاملComplex Interpolation between Hilbert, Banach and Operator Spaces
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 ...
متن کاملCharacterization of splitting for Fréchet-Hilbert spaces via interpolation
Based on the methods from interpolation theory we give a characterization of pairs (E,F ) of Fréchet-Hilbert spaces so that for each Fréchet-Hilbert space G each short exact sequence 0 −→ F −→ G −→ E −→ 0 splits. This characterization essentially depends on a key condition (S) of an interpolation nature. An equivalent description of (S) in terms of appropriate families of interpolation function...
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ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 1992
ISSN: 0004-2080
DOI: 10.1007/bf02384878