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<p>In this work, we establish new results on generalized perturbation theory for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(n\times n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>×</mo> <mi>n</mi> </mrow> </math></EquationSource> </InlineEquation> block operator matrices acting on a product of <i>n</i> Banach spaces. These results are formulated under certain topological assumptions on the Banach spaces or their duals. Furthermore, we investigate the generalized <i>E</i>-essential spectra of a <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(3\times 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation> operator matrix with unbounded entries, where <i>E</i> denotes a nonzero bounded linear operator.</p>

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Generalized E-essential spectra of \(n\times n\) block operator matrices and generalized perturbation theory

  • 期刊论文

  • 发表日期：

    2025年12月20日

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  • Yesmine Bahloul,
  • Bilel Krichen

摘要

In this work, we establish new results on generalized perturbation theory for \(n\times n\) n × n block operator matrices acting on a product of n Banach spaces. These results are formulated under certain topological assumptions on the Banach spaces or their duals. Furthermore, we investigate the generalized E-essential spectra of a \(3\times 3\) 3 × 3 operator matrix with unbounded entries, where E denotes a nonzero bounded linear operator.