Denjoy-Wolff theorems, Hilbert metric nonexpansive maps and reproduction-decimation operators |
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Authors: | Brian Lins |
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Institution: | Department of Mathematics, Rutgers University, USA |
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Abstract: | Let K be a closed cone with nonempty interior in a Banach space X. Suppose that is order-preserving and homogeneous of degree one. Let be a continuous, homogeneous of degree one map such that q(x)>0 for all x∈K?{0}. Let T(x)=f(x)/q(f(x)). We give conditions on the cone K and the map f which imply that there is a convex subset of ∂K which contains the omega limit set ω(x;T) for every x∈intK. We show that these conditions are satisfied by reproduction-decimation operators. We also prove that ω(x;T)⊂∂K for a class of operator-valued means. |
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Keywords: | Denjoy-Wolff theorems Positive operators Diffusion on fractals Dirichlet forms Hilbert metric Operator means |
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