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<p>We provide a positive answer to a question posed by Omid Zabeti in a recent work concerning the uaw-neighborhood of zero. We also investigate the relationships between uaw-compactness and sequential uaw-compactness. Furthermore, we study the weak topology generated by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( (E')^{a}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">(</mo> <msup> <mi>E</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> </mrow> <mi>a</mi> </msup> </math></EquationSource> </InlineEquation> on a Banach lattice <i>E</i> and its relationship with other modes of convergence. As a consequence, we obtain several interesting results for certain special classes of Banach lattices.</p>

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Some properties of unbounded absolute weak topology

  • 期刊论文

  • 发表日期：

    2025年10月22日

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  • Hassan Khabaoui,
  • Kamal El Fahri,
  • Jawad H’Michane

摘要

We provide a positive answer to a question posed by Omid Zabeti in a recent work concerning the uaw-neighborhood of zero. We also investigate the relationships between uaw-compactness and sequential uaw-compactness. Furthermore, we study the weak topology generated by \( (E')^{a}\) ( E ′ ) a on a Banach lattice E and its relationship with other modes of convergence. As a consequence, we obtain several interesting results for certain special classes of Banach lattices.