Turkish Journal of Mathematics
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.
DOI
10.55730/1300-0098.3242
Keywords
Primitive C*-algebra, B-Browder elements, socle, the generalized Weyl's theorem, perturbation
First Page
1927
Last Page
1944
Recommended Citation
KONG, Y, REN, Y, & JIANG, L (2022). Spectral theory of B-Weyl elements and the generalized Weyl's theorem in primitive C*-algebra. Turkish Journal of Mathematics 46 (5): 1927-1944. https://doi.org/10.55730/1300-0098.3242
