Joint and Generalized Spectral Radius of Upper Triangular Matrices with Entries in a Unital Banach Algebra

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.

کلیدواژه ها:

Banach algebra ، Upper Triangular Matrix ، Generalized Spectral Radius ، Joint Spectral Radius ، Geometric Joint Spectral Radius