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

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Gelfand–Phillips-Type Properties in Banach Lattices

  • 期刊论文

  • 发表日期：

    2025年11月18日

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  • Halimeh Ardakani,
  • Vinícius C. C. Miranda

摘要

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 Piñeiro, 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 the adjoint of every weakly compact taking values on E is disjoint p-summing.