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<p>This paper investigates the Cauchy dual in the context of closed-range operators, with special attention to weighted conditional operators on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^2(\Sigma )\)</EquationSource> </InlineEquation>. We establish some basic properties, such as binormality, centeredness, and power boundedness, of the Cauchy dual of weighted conditional operators. Furthermore, we investigate the connections between the Moore-Penrose inverse, Drazin inverse, and Cauchy dual for these types of operators.</p>

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Cauchy dual of conditional operators on \(L^2(\Sigma )\)

  • 期刊论文

  • 发表日期：

    2025年10月23日

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  • M. R. Jabbarzadeh,
  • Amani E. Kadhem

摘要

This paper investigates the Cauchy dual in the context of closed-range operators, with special attention to weighted conditional operators on \(L^2(\Sigma )\) . We establish some basic properties, such as binormality, centeredness, and power boundedness, of the Cauchy dual of weighted conditional operators. Furthermore, we investigate the connections between the Moore-Penrose inverse, Drazin inverse, and Cauchy dual for these types of operators.