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<p>Let <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal {A}\)</EquationSource> </InlineEquation> be an unital <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(C^*\)</EquationSource> </InlineEquation>-algebra and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(a,b \in \mathcal {A}\)</EquationSource> </InlineEquation>. In this paper, we provide a sufficient condition under which equation <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(a=bx\)</EquationSource> </InlineEquation> has a solution. We also provide a new characterizations of posinormal elements using the Moore-Penrose inverse. Furthermore, we define the notions of ascent and descent of an element to establish that the powers of a posinormal element remain posinormal under specific sufficient conditions.</p>

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Some remarkable properties of posinormal element in \(C^*\)-algebras

  • 期刊论文

  • 发表日期：

    2025年12月9日

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  • M. Deepak Maria Singh,
  • S. Veeramani

摘要

Let \(\mathcal {A}\) be an unital \(C^*\) -algebra and \(a,b \in \mathcal {A}\) . In this paper, we provide a sufficient condition under which equation \(a=bx\) has a solution. We also provide a new characterizations of posinormal elements using the Moore-Penrose inverse. Furthermore, we define the notions of ascent and descent of an element to establish that the powers of a posinormal element remain posinormal under specific sufficient conditions.