Logarithmic Interpolation Spaces between Quasi-Banach Spaces

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-...

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 ...

Weak Interpolation in Banach Spaces

Complex 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 ...

Distances between Banach spaces

Abstraca. The main object of the paper is to study the distance betwecn Banach spaces introduced by Kadets. For Banach spaccs Xand y. thc lGders distancc is denned to be rhe infimum of the Hausdorfl distance d(Bx, rr) betwecn the respoctive closed unit balls over all isomctric linear embeddings of f and yinto a common Banach space Z. This is comparcd with the Gromov-Hausdorff distance which is ...