Linear Maps Preserving Operators of Inner Local Spectral Radius Zero at Some Fixed Vector

2020 ◽  
Vol 17 (6) ◽  
Author(s):  
Constantin Costara
Keyword(s):  
Spectral Radius ◽  
Inner Local Spectral Radius ◽  
Linear Maps ◽  
Local Spectral Radius

scholarly journals Linear Maps Preserving Matrices of Local Spectral Radius Zero at a Fixed Vector

2019 ◽  
Vol 71 (4) ◽  
pp. 749-771
Author(s):  
Abdellatif Bourhim ◽  
Constantin Costara
Keyword(s):  
Spectral Radius ◽  
Nonzero Vector ◽  
Linear Maps ◽  
Local Spectral Radius ◽  
Matrix Spaces

AbstractIn this paper, we characterize linear maps on matrix spaces that preserve matrices of local spectral radius zero at some fixed nonzero vector.

scholarly journals Linear maps on Mn(C) preserving the local spectral radius

2008 ◽  
Vol 188 (1) ◽  
pp. 67-75 ◽  
Author(s):  
Abdellatif Bourhim ◽  
Vivien G. Miller
Keyword(s):  
Spectral Radius ◽  
Linear Maps ◽  
Local Spectral Radius

scholarly journals The local spectral radius of a nonnegative orbit of compact linear operators

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Mihály Pituk
Keyword(s):  
Banach Space ◽  
Spectral Radius ◽  
Additional Assumption ◽  
Real Banach Space ◽  
Linear Operators ◽  
Partial Ordering ◽  
Positive Eigenvector ◽  
Local Spectral Radius

AbstractWe consider orbits of compact linear operators in a real Banach space which are nonnegative with respect to the partial ordering induced by a given cone. The main result shows that under a mild additional assumption the local spectral radius of a nonnegative orbit is an eigenvalue of the operator with a positive eigenvector.

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