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arXiv · 2311.01974

Disjoint Dunford-Pettis-type properties in Banach lattices

Geraldo Botelho·José Lucas P. Luiz·Vinícius C. C. Miranda
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Abstract

New characterizations of the disjoint Dunford-Pettis property of order $p$ (disjoint $DPP_p$) are proved and applied to show that a Banach lattice of cotype $p$ has the disjoint $DPP_p$ whenever its dual has this property. The disjoint Dunford-Pettis$^*$ property of order $p$ (disjoint $DP^*P_p$) is thoroughly investigated. Close connections with the positive Schur property of order $p$, with the disjoint $DPP_p$, with the $p$-weak $DP^*$ property and with the positive $DP^*$ property of order $p$ are established. In a final section we study the polynomial versions of the disjoint $DPP_p$ and of the disjoint $DP^*P_p$.

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Geraldo Botelho, José Lucas P. Luiz, Vinícius C. C. Miranda. 2023-11-03. Disjoint Dunford-Pettis-type properties in Banach lattices. https://arxiv.org/abs/2311.01974

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