Joint and Generalized Spectral Radius of Upper Triangular Matrices with Entries in a Unital Banach Algebra
Journal: Sahand Communications in Mathematical Analysis (Vol.17, No. 3)Publication Date: 2020-07-01
Authors : Hamideh Mohammadzadehkan; Ali Ebadian; Kazem Haghnejad Azar;
Page : 175-188
Keywords : Banach algebra; Upper Triangular Matrix; Generalized Spectral Radius; Joint Spectral Radius; Geometric Joint Spectral Radius;
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,$Sigma$, $r_*left(Sigmaright)= hat{r}left(Sigmaright)$, 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.
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