To the theory of operators that are bounded on cones in weighted spaces of numerical sequences

The paper is devoted to the general problem of obtaining interpolation theorems for operators bounded on cones in normed spaces, and to some specific results pertaining to the particular problem of interpolation of operators bounded on cones in weighted spaces of numerical sequences. This setting is a natural generalization of the classical problem of interpolation of the boundness property of a linear operator that is bounded between two Banach couples. We introduce the general concept of a Banach triple of cones possessing the interpolation property with respect to a given Banach triple. We provide a sufficient conditions for a triple of cones $(Q_0,Q_1,Q)$ in weighted spaces of numerical sequences to possess the interpolation property with respect to a given Banach triple of weighted spaces of numerical sequences $(F_0,F_1,F)$. Appropriate interpolation theorems generalize the classical result about interpolation of linear operators in weighted spaces and are of interest for the theory of bases in Fréchet spaces.