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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Hille, S.C., Worm, D.T.H. Embedding of Semigroups of Lipschitz Maps into Positive Linear Semigroups on Ordered Banach Spaces Generated by Measures. Integr. equ. oper. theory 63, 351–371 (2009). https://doi.org/10.1007/s00020-008-1652-z
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DOI: https://doi.org/10.1007/s00020-008-1652-z