Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3242
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
First Page
1927
Last Page
1944
Recommended Citation
KONG, YINGYING; REN, YANXUN; and JIANG, LINING
(2022)
"Spectral theory of B-Weyl elements and the generalized Weyl's theorem in primitive C*-algebra,"
Turkish Journal of Mathematics: Vol. 46:
No.
5, Article 21.
https://doi.org/10.55730/1300-0098.3242
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss5/21
