University of MaraghehSahand Communications in Mathematical Analysis2322-580717320200701Joint and Generalized Spectral Radius of Upper Triangular Matrices with Entries in a Unital Banach Algebra1751883742010.22130/scma.2018.77951.362ENHamidehMohammadzadehkanDepartment of Mathematics, Faculty of Science, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.AliEbadianDepartment of Mathematics, Faculty of Science, Urmia University, Urmia, Iran.0000-0003-1067-6729KazemHaghnejad AzarDepartment of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.0000-0002-2591-3362Journal Article20171231In 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.https://scma.maragheh.ac.ir/article_37420_bddfc712abf56d71f714c37e0afce8c8.pdf