A characterization of the generalized spectral radius with Kronecker powers

Automatica ◽  
2011 ◽  
Vol 47 (7) ◽  
pp. 1530-1533 ◽  
Author(s):  
Jianhong Xu ◽  
Mingqing Xiao
Keyword(s):  
Spectral Radius ◽  
Generalized Spectral Radius

The A spectral radius characterization of some digraphs

2019 ◽  
Vol 563 ◽  
pp. 63-74 ◽  
Author(s):  
Jianping Liu ◽  
Xianzhang Wu ◽  
Jinsong Chen ◽  
Bolian Liu
Keyword(s):  
Spectral Radius

Generalized spectral radius and norm inequalities for Hilbert space operators

2015 ◽  
Vol 26 (12) ◽  
pp. 1550097
Author(s):  
Amer Abu-Omar ◽  
Fuad Kittaneh
Keyword(s):  
Hilbert Space ◽  
Spectral Radius ◽  
Operator Matrices ◽  
Norm Inequalities ◽  
Hilbert Space Operators ◽  
Generalized Spectral Radius

We apply spectral radius and norm inequalities to certain [Formula: see text] operator matrices to give simple proofs, refinements and generalizations of known norm inequalities. New norm inequalities are also given. Our analysis uncovers the interplay between different spectral radius and norm inequalities.

Spectral characterization of the radical in Banach and Jordan–Banach algebras

1993 ◽  
Vol 114 (1) ◽  
pp. 31-35 ◽  
Author(s):  
Bernard Aupetit
Keyword(s):  
Representation Theory ◽  
Spectral Radius ◽  
Jacobson Radical ◽  
Classical Result ◽  
Banach Algebras ◽  
Spectral Characterization ◽  
General Situation

If a is a n × n matrix such that a + m is invertible for every invertible a + m matrix m, then a = 0, by a classical result of Perlis [8]. Unfortunately the same result is not true in general for semi-simple rings as shown by T. Laffey. In the general situation of Banach algebras, Zemánek[12] has proved that a is in the Jacobson radical of A if and only if ρ(a+x) = ρ(x), for every x in A, where ρ denotes the spectral radius. More sophisticated characterizations of the radical were given in [4] and [3], theorem 5·3·1. The arguments used in all these situations depend heavily on representation theory.

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