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<p>In this paper, we introduce the concept of approximate Connes <i>I</i>-biprojectivity for Banach algebras, where <i>I</i> is a <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(w^*\)</EquationSource> </InlineEquation>-closed ideal on <i>A</i>. We explore several hereditary properties associated with this notion and provide illustrative examples that distinguish it from classical concepts. Finally, we offer a characterization of approximate Connes biprojectivity for upper triangular matrix Banach algebras and certain semigroup algebras.</p>

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An approximate notion of Connes biprojective dual Banach algebras related to a \(w^*\)-closed ideal

  • 期刊论文

  • 发表日期：

    2026年2月16日

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  • Ali Sarabagi,
  • Azizollah Babakhani,
  • Amir Sahami,
  • Mehdi Rostami

摘要

In this paper, we introduce the concept of approximate Connes I-biprojectivity for Banach algebras, where I is a \(w^*\) -closed ideal on A. We explore several hereditary properties associated with this notion and provide illustrative examples that distinguish it from classical concepts. Finally, we offer a characterization of approximate Connes biprojectivity for upper triangular matrix Banach algebras and certain semigroup algebras.