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<p>Let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_473_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathcal {X}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">X</mi> </math></EquationSource> </InlineEquation> be a complex Banach space, and let <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_473_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathcal {B}}({\mathcal {X}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">B</mi> <mo stretchy="false">(</mo> <mi mathvariant="script">X</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> be the algebra of all bounded linear operators on <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_473_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathcal {X}}.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">X</mi> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> In this paper, we characterize the general forms of surjective maps on <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_473_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathcal {B}}({\mathcal {X}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">B</mi> <mo stretchy="false">(</mo> <mi mathvariant="script">X</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> that preserve the dimension of fixed points of Jordan triple product of operators.</p>

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Maps preserving the dimension of fixed points of Jordan triple product of operators

  • 期刊论文

  • 发表日期：

    2025年8月27日

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  • Rixia Song,
  • Weijuan Shi

摘要

Let \({\mathcal {X}}\) X be a complex Banach space, and let \({\mathcal {B}}({\mathcal {X}})\) B ( X ) be the algebra of all bounded linear operators on \({\mathcal {X}}.\) X . In this paper, we characterize the general forms of surjective maps on \({\mathcal {B}}({\mathcal {X}})\) B ( X ) that preserve the dimension of fixed points of Jordan triple product of operators.