A note on the Banach lattice $c_0( \ell_2^n)$, its dual and its bidual - Lourenço, M.L.; Miranda, V.C.C. (Carpathian Mathematical Publications, 2023)
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 $l_{∞}(\ell_2^n)$ is an almost limited set.