The main purpose of this paper is to study some geometric properties on c 0 sum of the finite dimensional Banach lattice, ℓ n 2 and its dual. Among other results, we show that the Banach lattices c 0 (ℓ n 2 ) has the strong Gelfand-Philips property, but does not have the positive Grothendieck property. We also prove that the closed unit ball of l ∞ (ℓ n 2 ) is an almost limited set.

The main purpose of this paper is to study some geometric and topological properties of $c_0$-sum of the finite dimensional Banach lattice $\ell_2^n$, its dual and its bidual. Among other results, we show that the Banach lattice $c_0(\ell_2^n)$ 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.