@article {
author = {Mohammadzadehkan, Hamideh and Ebadian, Ali and Haghnejad Azar, Kazem},
title = {Joint and Generalized Spectral Radius of Upper Triangular Matrices with Entries in a Unital Banach Algebra},
journal = {Sahand Communications in Mathematical Analysis},
volume = {17},
number = {3},
pages = {175-188},
year = {2020},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2018.77951.362},
abstract = {In this paper, we discuss some properties of joint spectral {radius(jsr)} and generalized spectral radius(gsr) for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but some are different. For example for a bounded set of scalar matrices,$\Sigma$, $r_*\left(\Sigma\right)= \hat{r}\left(\Sigma\right)$, but for a bounded set of upper triangular matrices with entries in a Banach algebra($\Sigma$), $r_*\left(\Sigma\right)\neq\hat{r}\left(\Sigma\right)$. We investigate when the set is defective or not and equivalent properties for having a norm equal to jsr, too.},
keywords = {Banach algebra,Upper Triangular Matrix,Generalized Spectral Radius,Joint Spectral Radius,Geometric Joint Spectral Radius},
url = {https://scma.maragheh.ac.ir/article_37420.html},
eprint = {https://scma.maragheh.ac.ir/article_37420_7f123da849ba22fd0f27bd234a383849.pdf}
}