  Suppose $\Pi_1(E, F)$ is the space of all absolutely 1-summing operators
between two Banach spaces $E$ and $F$. We show that if $F$ has a copy of $c_0$,
then $\Pi_1(E, F)$ will have a copy of $c_0$, and under some conditions if $E$
has a copy of $\ell_1$ then $\Pi_1(E, F)$ would have a complemented copy of
$\ell_1$.
