Embedding of Semigroups of Lipschitz Maps into Positive Linear Semigroups on Ordered Banach Spaces Generated by Measures |
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Authors: | Sander C. Hille Daniël T. H. Worm |
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Affiliation: | (1) Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands |
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Abstract: | Interpretation, derivation and application of a variation of constants formula for measure-valued functions motivate our investigation of properties of particular Banach spaces of Lipschitz functions on a metric space and semigroups defined on their (pre)duals. Spaces of measures densely embed into these preduals. The metric space embeds continuously in these preduals, even isometrically in a specific case. Under mild conditions, a semigroup of Lipschitz transformations on the metric space then embeds into a strongly continuous semigroups of positive linear operators on these Banach spaces generated by measures. |
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Keywords: | KeywordHeading" >Mathematics Subject Classification (2000). Primary 46E27 Secondary 47H20, 47D06 |
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