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.KazemHaghnejad 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,$Sigma$, $r_*left(Sigmaright)= hat{r}left(Sigmaright)$, but for a bounded set of upper triangular matrices with entries in a Banach algebra($Sigma$), $r_*left(Sigmaright)neqhat{r}left(Sigmaright)$. 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_7f123da849ba22fd0f27bd234a383849.pdf