Scholarlink

<p>The characterization of special operators (or matrices), such as normal and self-adjoint (Hermitian) ones, through operator (or matrix) equations has been a topic of significant interest for a long time. In this paper, we explore equations involving products of an operator <i>X</i> and its adjoint <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(X^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>X</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>. We provide new characterizations of normal and Hermitian matrices using general matrix equations. We then extend and improve these results to operators on Hilbert spaces of any dimension. Moreover, we establish further characterizations of normal and self-adjoint operators (and matrices) based on our findings.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Solutions to the operator equation \(f(XX^*)=g(X^*X)\)

  • 期刊论文

  • 发表日期：

    2026年4月1日

查看全文
  • Rasoul Eskandari,
  • Mohammad Sal Moslehian,
  • Ali Talebi

摘要

The characterization of special operators (or matrices), such as normal and self-adjoint (Hermitian) ones, through operator (or matrix) equations has been a topic of significant interest for a long time. In this paper, we explore equations involving products of an operator X and its adjoint \(X^*\) X ∗ . We provide new characterizations of normal and Hermitian matrices using general matrix equations. We then extend and improve these results to operators on Hilbert spaces of any dimension. Moreover, we establish further characterizations of normal and self-adjoint operators (and matrices) based on our findings.