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

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

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

Mediterranean Journal of Mathematics ◽

10.1007/s00009-020-01644-x ◽

2020 ◽

Vol 17 (6) ◽

Author(s):

Constantin Costara

Keyword(s):

Spectral Radius ◽

Inner Local Spectral Radius ◽

Linear Maps ◽

Local Spectral Radius

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Linear Maps Preserving Operators of Local Spectral Radius Zero

Integral Equations and Operator Theory ◽

10.1007/s00020-012-1953-0 ◽

2012 ◽

Vol 73 (1) ◽

pp. 7-16 ◽

Cited By ~ 14

Author(s):

Constantin Costara

Keyword(s):

Spectral Radius ◽

Linear Maps ◽

Local Spectral Radius

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

Studia Mathematica ◽

10.4064/sm188-1-4 ◽

2008 ◽

Vol 188 (1) ◽

pp. 67-75 ◽

Cited By ~ 19

Author(s):

Abdellatif Bourhim ◽

Vivien G. Miller

Keyword(s):

Spectral Radius ◽

Linear Maps ◽

Local Spectral Radius

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

Mathematica Slovaca ◽

10.1515/ms-2015-0172 ◽

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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