A Note on Semigroups on Spaces of Continuous Functions and of Measures
نویسنده
چکیده
For Ω a Polish space we consider operator semigroups on the space Cb(Ω) of bounded, continuous functions and on the space M (Ω) of bounded Borel measures. The important fact here is that the dual of Cb(Ω) with the strict topology is M (Ω). We pursue the approach via bi-continuous semigroups, but we also show that the class of bi-continuous semigroups on Cb(Ω) with respect to the compact-open topology coincides with the class of equicontinuous semigroups with respect to the strict topology. If Ω is not Polish space this is not the case in general.
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