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

Abstract

Exploiting several ${\ell }_p$-factorization results for strictly singular operators, we study the strict singularity of the multiplication operator $L_A{R}_B:T\mapsto ATB$ on $\mathcal{L}(X)$ for various Banach spaces~$X$.

18 pages. A gap in the proof of Theorem 5.5 has been fixed