  A Banach space $X$ is reflexive if the Mackey topology $\tau(X^*,X)$ on $X^*$
agrees with the norm topology on $X^*$. Borwein [B] calls a Banach space $X$
{\it sequentially reflexive\/} provided that every $\tau(X^*,X)$ convergent
{\it sequence\/} in $X^*$ is norm convergent. The main result in [B] is that
$X$ is sequentially reflexive if every separable subspace of $X$ has separable
dual, and Borwein asks for a characterization of sequentially reflexive spaces.
Here we answer that question by proving
  \proclaim Theorem. {\sl A Banach space $X$ is sequentially reflexive if and
only if $\ell_1$ is not isomorphic to a subspace of $X$.}
