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<p>Conway and Hadwin introduced the notion of similarity domination for operators <i>S</i> and <i>T</i> on a Hilbert space and proved that if <i>T</i> similarity dominates <i>S</i>, then <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="MediaObjects/44146_2026_227_IEq1_HTML.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="120" Type="Linedraw" Width="74" /> </InlineMediaObject> </InlineEquation> for an entire function <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\varphi .\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>φ</mi> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> We study similarity domination in an arbitrary unital Banach algebra and prove their theorem for certain quotients of factor von Neumann algebras and for type <i>III</i> von Neumann algebras and for algebraic operators on a Banach space.</p>

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Similarity domination in operator algebras

  • 期刊论文

  • 发表日期：

    2026年2月19日

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  • Ali Zarringhalam,
  • Don Hadwin

摘要

Conway and Hadwin introduced the notion of similarity domination for operators S and T on a Hilbert space and proved that if T similarity dominates S, then for an entire function \(\varphi .\) φ . We study similarity domination in an arbitrary unital Banach algebra and prove their theorem for certain quotients of factor von Neumann algebras and for type III von Neumann algebras and for algebraic operators on a Banach space.