On some class of interpolation functors

As it is well known, the Gustavsson — Peetre construction, using the concept of unconditional convergence in Banach spaces, provides an important class of interpolation functors. In this paper, we define a new close construction, based on the use of the so-called random unconditional convergence. We find necessary and sufficient conditions, which being imposed on a generating function give us an interpolation functor defined on the category of Banach couples. It is shown that calculating the latter functor for a couple of Orlicz spaces results in the “natural” interpolation theorem. Moreover, we obtain conditions that guarantee the coincidence of this functor with the corresponding Gustavsson — Peetre functor, as well as with the Calderón — Lozanovskii method.