The Weyl's Theorem and Its Perturbations in Semisimple Banach Algebra

• 作者: Ying Ying KONG Li Ning JIANG Yan Xun REN
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（5）
• 页码范围: 675-688
• 页数: 14页
• 语种: 英文

摘要

Denote a semisimple Banach algebra with an identity e by A. This paper studies the Fredholm, Weyl and Browder spectral theories in a semisimple Banach algebra, and meanwhile considers the properties of the Fredholm element, the Weyl element and the Browder element. Further, for a∈A, we give the Weyl's theorem and the Browder's theorem for a, and characterize necessary and sufficient conditions that both a and f (a) satisfy the Weyl's theorem or the Browder's theorem, where f is a complex-valued function analytic on a neighborhood of σ(a). In addition, the perturbations of the Weyl's theorem and the Browder's theorem are investigated.