Arazy-Cwikel and Calder\'on-Mityagin type properties of the couples $(\ell^{p},\ell^{q})$, $0 \le p

We establish Arazy-Cwikel type properties for the family of couples (l, l), 0 ≤ p < q ≤ ∞, and show that (l, l) is a Calderón-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 ≤ ∞ and obtain a simple positive solution of a Levitina-Sukochev-Zanin problem, clarifying its connections with whether (l, l) has the Calderón-Mityagin property or not.

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