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 $L_p$ spaces. To this end, the structure of strictly singular non-compact operators between $L_p-L_q$ 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.

arXiv comment20 pages. To appear in Adv. Math

References in corpus (1)

• Rigidity of composition operators on the Hardy space $H^p$