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<p>In this paper, we introduce the concept of posinormal elements in a <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1204_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-algebra. The characterization of these elements is achieved using Douglas’s theorem. We also present sufficient conditions under which the equation <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1204_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">\( a = a^*x\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>a</mi> <mo>=</mo> <msup> <mi>a</mi> <mo>∗</mo> </msup> <mi>x</mi> </mrow> </math></EquationSource> </InlineEquation> can be solved. Furthermore, we provide a sufficient condition for a hyponormal element to be posinormal. Finally, we study the relationship between invertibility and posinormality and we establish some results about the stability nature of posinormal element.</p>

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Posinormal element in \(C^*\)-algebras

  • 期刊论文

  • 发表日期：

    2025年3月10日

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  • M. Deepak Maria Singh,
  • S. Veeramani

摘要

In this paper, we introduce the concept of posinormal elements in a \(C^*\) C ∗ -algebra. The characterization of these elements is achieved using Douglas’s theorem. We also present sufficient conditions under which the equation \( a = a^*x\) a = a ∗ x can be solved. Furthermore, we provide a sufficient condition for a hyponormal element to be posinormal. Finally, we study the relationship between invertibility and posinormality and we establish some results about the stability nature of posinormal element.