Document Type : Research Paper


1 Department of Mathematics, Faculty of Science, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.

2 Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran.

3 Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.


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.


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