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 Lp−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.

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