  The main purpose of this paper is to study some geometric and topological
properties on $ c_0$ sum of the finite dimensional Banach lattice $\ell_2^n$,
its dual and its bidual. Among other results, we show that the Banach lattices
$c_0(\ell_2^n)$ has the strong Gelfand-Philips property, but does not have the
positive Grothendieck property. We also prove that the closed unit ball of
$l_{\infty}(\ell_2^n)$ is an almost limited set.

Functional Analysis