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<p>In this paper, we first give another characterization for S-Weyl’s using a newly defined spectrum. Then, we apply it to several types of special operators. Meanwhile, we obtain the properties of those operators whose Riesz–Dunford functional calculus satisfies S-Weyl’s theorem. Besides, we explore S-Weyl’s theorem for operators under compact perturbations. Finally, the relationships between the stability and the functions of operators for S-Weyl’s theorem are discussed.</p>

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S-Weyl’s Theorem for Functions of Operators and Its Stability Under Compact Perturbations

  • 期刊论文

  • 发表日期：

    2025年10月21日

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  • Lili Yang,
  • Xiaohong Cao

摘要

In this paper, we first give another characterization for S-Weyl’s using a newly defined spectrum. Then, we apply it to several types of special operators. Meanwhile, we obtain the properties of those operators whose Riesz–Dunford functional calculus satisfies S-Weyl’s theorem. Besides, we explore S-Weyl’s theorem for operators under compact perturbations. Finally, the relationships between the stability and the functions of operators for S-Weyl’s theorem are discussed.