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arXiv · 2507.16811

Gelfand-Phillips-type properties in Banach lattices

Halimeh Ardakani·Vinícius C. C. Miranda
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Abstract

We study $p$-limited and almost $p$-limited sets in Banach lattices and their connections with relatively $p$-compact and relatively compact sets. We investigate the weak and the strong Gelfand-Phillips property of order $p$, as well as the $p$-GP property introduced by Delgado and Pi\~neiro, providing conditions under which these properties may coincide. Additionally, we prove that a Banach lattice $E$ is a KB-space if and only if every almost $p$-limited set in $E$ is relatively weakly compact if and only if every the adjoint of a weakly compact taking values on $E$ is disjoint $p$-summing.

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Halimeh Ardakani, Vinícius C. C. Miranda. 2025-07-22. Gelfand-Phillips-type properties in Banach lattices. https://arxiv.org/abs/2507.16811

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