ON SOME CLASS OF INTERPOLATION FUNCTORS

Abstract

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 Calderon Lozanovskii method.