Strictly singular multiplication operators on $\mathcal L(X)$

TL;DR

This paper investigates the strict singularity of multiplication operators on the space of bounded linear operators over Banach spaces, using $ ext{ell}_p$-factorization techniques to analyze their properties.

Contribution

It introduces new criteria for strict singularity of multiplication operators on $ ext{L}(X)$ based on $ ext{ell}_p$-factorization results for Banach spaces.

Findings

Characterization of strict singularity for multiplication operators

Application of $ ext{ell}_p$-factorization techniques

Results applicable to various Banach spaces

Abstract

Exploiting several $\ell_p$-factorization results for strictly singular operators, we study the strict singularity of the multiplication operator $L_A R_B\colon T\mapsto ATB$ on $\mathcal L(X)$ for various Banach spaces~$X$.