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Roman Drnovˇsek *K@I BH JDA IFA?JH= H=@EKI B FIEJELA FAH=JHI

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Roman Drnovˇsek

Bounds for the spectral radius of positive operators

Comment.Math.Univ.Carolinae 41,3 (2000) 459-467.

Abstract: Letf be a non-zero positive vector of a Banach latticeL, and letT be a positive linear operator onLwith the spectral radiusr(T). We find some groups of assumptions onL,T andf under which the inequalities

sup{c≥0 :T f ≥cf} ≤r(T)≤inf{c≥0 :T f ≤cf}

hold. An application of our results gives simple upper and lower bounds for the spectral radius of a product of positive operators in terms of positive eigenvectors corresponding to the spectral radii of given operators. We thus extend the matrix result obtained by Johnson and Bru which was the motivation for this paper.

Keywords: Banach lattices, positive operators, spectral radius AMS Subject Classification: 46B42, 47B65, 47A10

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