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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 66, Issue 3


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

Mihály Pituk
Published Online: 2016-08-26 | DOI: https://doi.org/10.1515/ms-2015-0172


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.


  • [1]

    Berman, A.—Plemmons, R.: Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979.Google Scholar

  • [2]

    Chen, M.—Chen, X.-Y.—Hale, J. K.: Structural stability for time-periodic one-dimensional parabolic equations, J. Differential Equations 96 (1992), 355–418.Google Scholar

  • [3]

    Conway, J. B.: A Course in Functional Analysis (2nd ed.), Springer-Verlag, New York, 1990.Google Scholar

  • [4]

    Krasnoselskij, M. A.—Lifshits, Je. A.—Sobolev, A. V.: Positive Linear Systems. The Method of Positive Operators, Heldermann Verlag, Berlin, 1989.Google Scholar

  • [5]

    Krein, M. G.—Rutman, M. A.: Linear operators leaving a cone invariant in a Banach space, Uspekhi Mat. Nauk 3(23) (1948), No. 1, 3–95 (Russian) [English transl.: Amer. Math. Soc. Transl. 26, Amer. Math. Soc., Providence, RI, 1950].Google Scholar

  • [6]

    Müller, V.: Spectral Theory of Linear Operators and Spectral System in Banach Algebras (2nd ed.), Birkhäuser, Basel, 2007.Google Scholar

  • [7]

    Obaya, R.—Pituk, M.: A variant of the Krein-Rutman theorem for Poincaré difference equations, J. Difference Equ. Appl. 18 (2012), 1751–1762.Google Scholar

  • [8]

    Zeidler, E.: Nonlinear Functional Analysis and its Applications I. Fixed-Point Theorems, Springer-Verlag, New York, 1986.Google Scholar

About the article

Received: 2013-08-08

Accepted: 2014-01-17

Published Online: 2016-08-26

Published in Print: 2016-06-01

Citation Information: Mathematica Slovaca, Volume 66, Issue 3, Pages 707–714, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0172.

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