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<p>Let <i>A</i> be a bounded operator acting in a separable complex Hilbert space. We define the operator gamma function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Gamma (A)\)</EquationSource> </InlineEquation> of <i>A</i>, which is a generalization of the classical Euler gamma function. We derive norm estimates for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Gamma (A)\)</EquationSource> </InlineEquation> and some related special functions, as well as establish perturbation bounds.</p>

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Perturbation of the operator gamma function

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • Michael Gil’

摘要

Let A be a bounded operator acting in a separable complex Hilbert space. We define the operator gamma function \(\Gamma (A)\) of A, which is a generalization of the classical Euler gamma function. We derive norm estimates for \(\Gamma (A)\) and some related special functions, as well as establish perturbation bounds.