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<p>The paper explores the Aluthge transformation and its generalizations, as well as the extension of the operator transformation propositionosed by Patel–Tanahashi–Uchiyama for the class of EP operators using matrix representations of operators. Additionally, we derive several applications of these findings to the conditional type operator <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1262_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="65" /> </InlineMediaObject> <EquationSource Format="TEX">\(M_{w}EM_{u}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>M</mi> <mi>w</mi> </msub> <mi>E</mi> <msub> <mi>M</mi> <mi>u</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> on <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1262_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^2(\Sigma ),\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Σ</mi> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> where <i>E</i> represents the conditional expectation operator.</p>

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Applications of polar decomposition of EP operators

  • 期刊论文

  • 发表日期：

    2025年6月29日

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  • Mehdi Mohammadzadeh Karizaki,
  • Morteza Sohrabi

摘要

The paper explores the Aluthge transformation and its generalizations, as well as the extension of the operator transformation propositionosed by Patel–Tanahashi–Uchiyama for the class of EP operators using matrix representations of operators. Additionally, we derive several applications of these findings to the conditional type operator \(M_{w}EM_{u}\) M w E M u on \(L^2(\Sigma ),\) L 2 ( Σ ) , where E represents the conditional expectation operator.