  By a result of Johnson, the Banach space $F=(\bigoplus_{n=1}^\infty
\ell_1^n)_{\ell_\infty}$ contains a complemented copy of $\ell_1$. We identify
$F$ with a complemented subspace of the space of (bounded, linear) operators on
the reflexive space $(\bigoplus_{n=1}^\infty \ell_1^n)_{\ell_p}$ ($p\in
(1,\infty))$, thus giving a negative answer to the problem posed in the
monograph of Diestel and Uhl which asks whether the space of operators on a
reflexive Banach space is Grothendieck.
