Arazy-Cwikel and Calderon-Mityagin type properties of the couples (lp, lq), 0 ≤ p ≤ q ≤ ∞

Abstract

We establish Arazy-Cwikel type properties for the family of couples (l(p), l(q)), 0 <= p < q <= infinity, and show that (l(p), l(q)) is a Calderon-Mityagin couple if and only if q >= 1. Moreover, we identify interpolation orbits of elements with respect to this couple for all p and q such that 0 <= p < q <= infinity and obtain a simple positive solution of a Levitina-Sukochev-Zanin problem, clarifying its connections with whether (l(p), l(q)) has the Calderon-Mityagin property or not.