Published online by Cambridge University Press: 18 January 2016
A recent result of Leung (Proceedings of the American Mathematical Society, 2015) states that the Banach algebra ℬ(X) of bounded, linear operators on the Banach space X = (⊕n∈$\mathbb{N}$ ℓ∞n)ℓ1 contains a unique maximal ideal. We show that the same conclusion holds true for the Banach spaces X = (⊕n∈
$\mathbb{N}$ ℓ∞n)ℓp and X = (⊕n∈
$\mathbb{N}$ ℓ1n)ℓp whenever p ∈ (1, ∞).