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<p>In this article, we study the isomorphism problem for the algebras of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\Phi\)</EquationSource> </InlineEquation>-pseudofunctions and <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\Phi\)</EquationSource> </InlineEquation>-pseudomeasures, denoted by <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(PF_\Phi (G)\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(PM_\Phi (G),\)</EquationSource> </InlineEquation> respectively. More precisely, for a certain class of Young functions <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\Phi ,\)</EquationSource> </InlineEquation> we prove that if there exists an isometric isomorphism between <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(PF_\Phi (G_1)\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(PF_\Phi (G_2),\)</EquationSource> </InlineEquation> or between <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(PM_\Phi (G_1)\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(PM_\Phi (G_2),\)</EquationSource> </InlineEquation> then <InlineEquation ID="IEq15"> <EquationSource Format="TEX">\(G_1\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq16"> <EquationSource Format="TEX">\(G_2\)</EquationSource> </InlineEquation> are isomorphic as topological groups. In addition, we present an Orlicz version of Parrott’s isomorphism theorem.</p>

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Isomorphism theorems for the algebras of \(\Phi\)-pseudofunctions and \(\Phi\)-pseudomeasures

  • 期刊论文

  • 发表日期：

    2026年3月13日

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  • Arvish Dabra,
  • N. Shravan Kumar

摘要

In this article, we study the isomorphism problem for the algebras of \(\Phi\) -pseudofunctions and \(\Phi\) -pseudomeasures, denoted by \(PF_\Phi (G)\) and \(PM_\Phi (G),\) respectively. More precisely, for a certain class of Young functions \(\Phi ,\) we prove that if there exists an isometric isomorphism between \(PF_\Phi (G_1)\) and \(PF_\Phi (G_2),\) or between \(PM_\Phi (G_1)\) and \(PM_\Phi (G_2),\) then \(G_1\) and \(G_2\) are isomorphic as topological groups. In addition, we present an Orlicz version of Parrott’s isomorphism theorem.