Interpolation and extrapolation of strictly singular operators between L-p spaces

Abstract

We study the interpolation and extrapolation properties of strictly singular operators between different Lp spaces. To this end, the structure of strictly singular non-compact operators between L-p Lq spaces is analyzed. Among other things, we clarify the relation between strict singularity and the L-characteristic set of an operator. In particular, Krasnoselskii's interpolation theorem for compact operators is extended to the class of strictly singular operators. (C) 2017 Elsevier Inc.