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Abstract <p> In the paper, a new class of universal <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3043_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^*\)</EquationSource> </InlineEquation>-algebras, namely, Blaschke <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3043_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^*\)</EquationSource> </InlineEquation>-algebras, are constructed, for which the relations between generators are defined by a family of finite Blaschke products. Two approaches to constructing a universal object are proposed, one of which is related to the inductive limit of Toeplitz algebras, and the other to an isometric representation of the uniform Blaschke algebra. <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3043_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^*\)</EquationSource> </InlineEquation>-algebras generated by isometric representations of a Blaschke algebra in the algebra of bounded linear operators on generalized Hardy spaces with a probability measure and, in particular, with a Haar measure are considered in detail. </p>

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Family of Finite Blaschke Products in \(C^*\)-Algebras

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • T. A. Grigoryan,
  • A. Yu. Kuznetsova

摘要

Abstract

In the paper, a new class of universal \(C^*\) -algebras, namely, Blaschke \(C^*\) -algebras, are constructed, for which the relations between generators are defined by a family of finite Blaschke products. Two approaches to constructing a universal object are proposed, one of which is related to the inductive limit of Toeplitz algebras, and the other to an isometric representation of the uniform Blaschke algebra. \(C^*\) -algebras generated by isometric representations of a Blaschke algebra in the algebra of bounded linear operators on generalized Hardy spaces with a probability measure and, in particular, with a Haar measure are considered in detail.