  A recent result of Leung (Proceedings of the American Mathematical Society,
to appear) states that the Banach algebra $\mathscr{B}(X)$ of bounded, linear
operators on the Banach space
$X=\bigl(\bigoplus_{n\in\mathbb{N}}\ell_\infty^n\bigr)_{\ell_1}$ contains a
unique maximal ideal. We show that the same conclusion holds true for the
Banach spaces $X=\bigl(\bigoplus_{n\in\mathbb{N}}\ell_\infty^n\bigr)_{\ell_p}$
and $X=\bigl(\bigoplus_{n\in\mathbb{N}}\ell_1^n\bigr)_{\ell_p}$ whenever
$p\in(1,\infty)$.
