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The main purpose of this paper is to study some geometric and topologicalproperties 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 thepositive Grothendieck property. We also prove that the closed unit ball of$l_{\infty}(\ell_2^n)$ is an almost limited set.

A note on the Banach lattice $c_0( \ell_2^n)$, its dual and its bidual