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<p>In this paper, we provide a correct and complete proof of a result obtained by K. El Fahri and M. Moussa [Domination by positive Dunford–Pettis completely continuous operators. Afr. Mat. 27, 1311–1319 (2016)]. Moreover, we present a refinement of some other results. Among other things, we establish that the convex solid hull of each almost Dunford Pettis set of a Banach lattice <i>E</i> is also almost Dunford Pettis set. Additionally, we establish that the convex solid hull of each Dunford–Pettis set of <i>E</i> is Dunford–Pettis if and only if one of the equivalent conditions is satisfied: (1) The order intervals of <i>E</i> are Dunford–Pettis sets; (2) Every almost Dunford–Pettis set of <i>E</i> is a Dunford–Pettis set.</p>

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A note on the Dunford–Pettis completely continuous operators

  • 期刊论文

  • 发表日期：

    2026年2月16日

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  • Aziz Elbour,
  • Khalid Bouras

摘要

In this paper, we provide a correct and complete proof of a result obtained by K. El Fahri and M. Moussa [Domination by positive Dunford–Pettis completely continuous operators. Afr. Mat. 27, 1311–1319 (2016)]. Moreover, we present a refinement of some other results. Among other things, we establish that the convex solid hull of each almost Dunford Pettis set of a Banach lattice E is also almost Dunford Pettis set. Additionally, we establish that the convex solid hull of each Dunford–Pettis set of E is Dunford–Pettis if and only if one of the equivalent conditions is satisfied: (1) The order intervals of E are Dunford–Pettis sets; (2) Every almost Dunford–Pettis set of E is a Dunford–Pettis set.