Title of article :
Joint and Generalized Spectral Radius of Upper Triangular Matrices with Entries in a Unital Banach Algebra
Author/Authors :
Mohammadzadehkan ، Hamideh Department of Mathematics - Faculty of Science - Payame Noor University , Ebadian ، Ali Department of Mathematics - Faculty of Science - Urmia University , Haghnejad Azar ، Kazem Department of Mathematics - University of Mohaghegh Ardabili
Abstract :
In this paper, we discuss some properties of joint spec tral 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,Σ, r∗ (Σ) = ˆr (Σ), but for a bounded set of upper triangular matrices with entries in a Banach algebra(Σ), r∗ (Σ) ̸= ˆr (Σ). We investigate when the set is defective or not and equivalent properties for having a norm equal to jsr, too.
Keywords :
Banach Algebra , Upper Triangular Matrix , Generalized Spectral Radius , Joint Spectral Radius , Geometric Joint Spectral Radius
Journal title :
Sahand Communications in Mathematical Analysis
Journal title :
Sahand Communications in Mathematical Analysis
