Interpolative ideal procedures, interpolation, and applications to approximation quantities

Abstract

This paper deals with a generalization of a certain interpolative procedure introduced by U. Matter [9] by which from given Banach ideals A and B a new scale of Banach ideals (A,B)' is generated. In particular we elaborate the connection of our construction to interpolation theory. As an application we consider the ideal of (p,')-absolutely continuous operators which occurs when A is the class of p-summing operators and B is the class of all operators. We characterize (p,')-absolutely continuous operators by a special factorization property through a suitable interpolation space. We also give some applications to approximation quantities and entropy numbers.