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<p>We study operators that carry disjoint bounded subsets of a Banach lattice intocompact, weakly compact, and limited subsets of a Banach space.Surprisingly, these operators behave differently from classical compact, weakly compact,and limited operators.Examples demonstrating that these operators differ from the correspondingclassical operators are presented.We introduce and study d-Andrews operators,which carry disjoint bounded sets into Dunford–Pettis sets.The domination problem and norm completeness are discussed for the above-mentioned operators.It is shown that, in general, the domination problem for d-limited operators has a negative solution.Natural conditions on the range are provided that yieldpositive solutions to the domination problem for d-limited and d-Andrews operators.It is shown that the linear spans of d-compact and d-weakly compact positive operators are completewith respect to their enveloping norms.The “almost versions” are also investigated.</p>

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\( \mathrm{d} \)-Operators in Banach Lattices

  • 期刊论文

  • 发表日期：

    2025年11月24日

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  • E. Yu. Emelyanov,
  • N. Erkurşun-Özcan,
  • S. G. Gorokhova

摘要

We study operators that carry disjoint bounded subsets of a Banach lattice intocompact, weakly compact, and limited subsets of a Banach space.Surprisingly, these operators behave differently from classical compact, weakly compact,and limited operators.Examples demonstrating that these operators differ from the correspondingclassical operators are presented.We introduce and study d-Andrews operators,which carry disjoint bounded sets into Dunford–Pettis sets.The domination problem and norm completeness are discussed for the above-mentioned operators.It is shown that, in general, the domination problem for d-limited operators has a negative solution.Natural conditions on the range are provided that yieldpositive solutions to the domination problem for d-limited and d-Andrews operators.It is shown that the linear spans of d-compact and d-weakly compact positive operators are completewith respect to their enveloping norms.The “almost versions” are also investigated.