Arazy–Cwikel and Calderón–Mityagin type properties of the couples $$(\ell ^{p},\ell ^{q})$$, $$0\le p<q\le \infty $$

We establish Arazy–Cwikel type properties for the family of couples $$ (\ell ^{p},\ell ^{q})$$ , $$0\le p<q\le \infty and show that $$(\ell ^{q}) is a Calderón–Mityagin couple if only $$q\ge 1$$ . Moreover, we identify interpolation orbits elements with respect to this all p q such obtain simple positive solution Levitina–Sukochev–Zanin problem, clarifying its connections whether has property or not.