  A closed subspace $S$ of $\ell_\infty$ is said to be a
\emph{$\ell_\infty$-Grothendieck subspace} if $c_0\subset S$ (hence
$\ell_\infty\subset S^{**}$) and every $\sigma(S^*,S)$-convergent sequence in
$S^*$ is $\sigma(S^*,\ell_\infty)$-convergent. Here we give examples of closed
subspaces of $\ell_\infty$ containing $c_0$ which are or fail to be
$\ell_\infty$-Grothendieck.
