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<p>In this paper, we introduce the concept of the gap between two linear subspaces in asymmetric normed spaces as a generalization of Kato’s definition in the normed case. We analyze various properties of this novel concept and explore its applications to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((r, \bar{r})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>r</mi> <mo>,</mo> <mover accent="true"> <mrow> <mi>r</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-closed operators between asymmetric normed spaces, proving results related to this class of operators.</p>

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The gap between asymmetric normed subspaces and its applications

  • 期刊论文

  • 发表日期：

    2026年3月18日

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  • Hassan Zine,
  • Abdelhamid Tallab,
  • Ştefan Cobzaş

摘要

In this paper, we introduce the concept of the gap between two linear subspaces in asymmetric normed spaces as a generalization of Kato’s definition in the normed case. We analyze various properties of this novel concept and explore its applications to \((r, \bar{r})\) ( r , r ¯ ) -closed operators between asymmetric normed spaces, proving results related to this class of operators.