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<p>Following the concept of <i>L</i>-sets in the dual of a Banach space and using the class of almost Dunford-Pettis sets in a Banach lattice, the notion of <i>L</i>-almost Dunford-Pettis sets is introduced and studied. As an application, Banach lattices with the strong relatively compact Dunford-Pettis property, weak Dunford-Pettis property, and positive Schur property are characterized. Moreover, the behavior of almost Dunford-Pettis completely continuous operators is described and then the domination problem and the adjoint problem for this class of operators are addressed.</p>

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Dunford-Pettis like Sets with Applications to Spaces of Operators

  • 期刊论文

  • 发表日期：

    2025年2月14日

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  • Halimeh Ardakani,
  • Vinícius C. C. Miranda

摘要

Following the concept of L-sets in the dual of a Banach space and using the class of almost Dunford-Pettis sets in a Banach lattice, the notion of L-almost Dunford-Pettis sets is introduced and studied. As an application, Banach lattices with the strong relatively compact Dunford-Pettis property, weak Dunford-Pettis property, and positive Schur property are characterized. Moreover, the behavior of almost Dunford-Pettis completely continuous operators is described and then the domination problem and the adjoint problem for this class of operators are addressed.