Ideals of operators on $(\oplus \ell^\infty(n))_{\ell^1}$

Abstract

The unique maximal ideal in the Banach algebra $L(E)$, $E = (\oplus \ell^\infty(n))_{\ell^1}$, is identified. The proof relies on techniques developed by Laustsen, Loy and Read and a dichotomy result for operators mapping into $L^1$ due to Laustsen, Odell, Schlumprecht and Zs\'{a}k.