Spectral theory of B-Weyl elements and the generalized Weyl's theorem in primitive C*-algebra

Authors: YINGYING KONG, YANXUN REN, LINING JIANG

Abstract: Let $\mathcal{A}$ be a unital primitive C*-algebra. This paper studies the spectral theories of B-Weyl elements and B-Browder elements in $\mathcal{A}$, including the spectral mapping theorem and a characterization of B-Weyl spectrum. In addition, we characterize the generalized Weyl's theorem and the generalized Browder's theorem for an element $a\in\mathcal{A}$ and $f(a)$, where $f$ is a complex-valued function analytic on a neighborhood of $\sigma(a)$. What's more, the perturbations of the generalized Weyl's theorem under the socle of $\mathcal{A}$ and quasinilpotent element are illustrated.

Keywords: Primitive C*-algebra, B-Browder elements, socle, the generalized Weyl's theorem, perturbation

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