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<p>In this paper, we introduce a new class of operators called <i>k</i>-quasi skew <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\left( A,m\right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi>A</mi> <mo>,</mo> <mi>m</mi> </mfenced> </math></EquationSource> </InlineEquation>-symmetric operators, which extends the class of skew <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\left( A,m\right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi>A</mi> <mo>,</mo> <mi>m</mi> </mfenced> </math></EquationSource> </InlineEquation>-symmetric operators studied by R. Rabaoui (Filomat, 36 (10) (2022), 3261–3278). A matrix characterization, stability under nilpotent perturbations, and several spectral properties are established. The notion is also extended to multivariable operator tuples.</p>

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Developments of a generalized Skew (A, m)-symmetric operators

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Imene Djaber,
  • Messaoud Guesba

摘要

In this paper, we introduce a new class of operators called k-quasi skew \(\left( A,m\right) \) A , m -symmetric operators, which extends the class of skew \(\left( A,m\right) \) A , m -symmetric operators studied by R. Rabaoui (Filomat, 36 (10) (2022), 3261–3278). A matrix characterization, stability under nilpotent perturbations, and several spectral properties are established. The notion is also extended to multivariable operator tuples.