# Interpolation and extrapolation of strictly singular operators between $L_p$ spaces

## TL;DR

This paper investigates the behavior of strictly singular operators between different Lp spaces, extending classical interpolation results and analyzing their structure and characteristics.

## Contribution

It provides a detailed analysis of strictly singular operators between Lp spaces and extends Krasnoselskii's interpolation theorem to this class.

## Key findings

- Extended Krasnoselskii's theorem to strictly singular operators
- Clarified the relation between strict singularity and L-characteristic set
- Analyzed the structure of non-compact strictly singular operators

## 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.