  A theorem of Giesy and James states that $c_0$ is finitely representable in
James' quasi-reflexive Banach space $J_2$. We extend this theorem to the $p$th
quasi-reflexive James space $J_p$ for each $p \in (1,\infty)$. As an
application, we obtain a new closed ideal of operators on $J_p$, namely the
closure of the set of operators that factor through the complemented subspace
$(\ell_\infty^1 \oplus \ell_\infty^2 \oplus...\oplus \ell_\infty^n
\oplus...)_{\ell_p}$ of $J_p$.

Functional Analysis;Operator Algebras