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

  • Mihály Pituk EMAIL logo
Published/Copyright: August 26, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 3

Abstract

We 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.

MSC 2010: Primary 47A11; Secondary 39A10
keywords: compact linear operator; orbit; local spectral radius; cone; eigenvalue

This work was supported by the Hungarian National Foundation for Scientific Research (OTKA) Grant No. K. 101217.

(Communicated by Werner Timmermann)

References

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Received: 2013-8-8
Accepted: 2014-1-17
Published Online: 2016-8-26
Published in Print: 2016-6-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0172
Keywords for this article
compact linear operator; orbit; local spectral radius; cone; eigenvalue

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