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• W2051733130 abstract "This paper concerns the question whether the cone spectral radius $r_C(f)$ of a continuous compact order-preserving homogenous map $fcolon Cto C$ on a closed cone $C$ in Banach space $X$ depends continuously on the map. Using the fixed point index we show that if there exists $0<a_1<a_2<a_3<ldots$ not in the cone spectrum, $sigma _C(f)$, and $lim _{kto infty } a_k = r_C(f)$, then the cone spectral radius is continuous. An example is presented showing that if such a sequence $(a_k)_k$ does not exist, continuity may fail. We also analyze the cone spectrum of continuous order-preserving homogeneous maps on finite dimensional closed cones. In particular, we prove that if $C$ is a polyhedral cone with $m$ faces, then $sigma _C(f)$ contains at most $m-1$ elements, and this upper bound is sharp for each polyhedral cone. Moreover, for each nonpolyhedral cone there exist maps whose cone spectrum is infinite." @default.
• W2051733130 created "2016-06-24" @default.
• W2051733130 creator A5034034772 @default.
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• W2051733130 date "2013-04-08" @default.
• W2051733130 modified "2023-10-02" @default.
• W2051733130 title "Continuity of the cone spectral radius" @default.
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• W2051733130 doi "https://doi.org/10.1090/s0002-9939-2013-11520-0" @default.
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