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<p>The goal of this note is to give a positive answer to the problem 4.11 in [<i>Almost BS-compact operators and domination problem, Mediterr. J. Math.</i> 18, 258 (2021)]. More precisely, we proved that if a positive operator <i>R</i> on a Banach lattice <i>E</i> is dominated by an almost <i>BS</i>-compact operator <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1300_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="83" /> </InlineMediaObject> <EquationSource Format="TEX">\(T: E \rightarrow E\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>T</mi> <mo>:</mo> <mi>E</mi> <mo stretchy="false">→</mo> <mi>E</mi> </mrow> </math></EquationSource> </InlineEquation>, then <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1300_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(R^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>R</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> is almost <i>BS</i>-compact.</p>

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On an open question concerning the domination problem in the class of almost BS-compact operators

  • 期刊论文

  • 发表日期：

    2025年4月18日

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  • Mohamed Hajji

摘要

The goal of this note is to give a positive answer to the problem 4.11 in [Almost BS-compact operators and domination problem, Mediterr. J. Math. 18, 258 (2021)]. More precisely, we proved that if a positive operator R on a Banach lattice E is dominated by an almost BS-compact operator \(T: E \rightarrow E\) T : E → E , then \(R^2\) R 2 is almost BS-compact.