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<p>In the present paper, the notion of weak degree of nondensifiability, <i>w</i>-DND, is introduced. Likewise, we analyze its main properties, and we also prove that the <i>w</i>-DND is actually an upper bound for any measure of weak noncompactness. Moreover, for the De Blasi measure of weak noncompactness, such an upper bound is sharp. As an application of our results, we characterize both Schur and Dunford–Pettis properties of a Banach space in terms of the <i>w</i>-DND, which turns out this new concept into a useful tool in functional analysis.</p>

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Weak nondensifiability in Banach spaces

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Gonzalo García,
  • Gaspar Mora

摘要

In the present paper, the notion of weak degree of nondensifiability, w-DND, is introduced. Likewise, we analyze its main properties, and we also prove that the w-DND is actually an upper bound for any measure of weak noncompactness. Moreover, for the De Blasi measure of weak noncompactness, such an upper bound is sharp. As an application of our results, we characterize both Schur and Dunford–Pettis properties of a Banach space in terms of the w-DND, which turns out this new concept into a useful tool in functional analysis.