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arXiv · 2011.09319

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

M. L. Lourenço·V. C. C. Miranda
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Abstract

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.

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M. L. Lourenço, V. C. C. Miranda. 2020-11-18. A note on the Banach lattice $c_0( \ell_2^n)$, its dual and its bidual. https://arxiv.org/abs/2011.09319

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