Power bounded weighted composition operators on function spaces defined by local properties
2019
Abstract We study power boundedness and related properties such as mean ergodicity for (weighted) composition operators on function spaces defined by local properties. As a main application of our general approach we characterize when (weighted) composition operators are power bounded, topologizable, and (uniformly) mean ergodic on kernels of certain linear partial differential operators including elliptic operators as well as non-degenerate parabolic operators. Moreover, under mild assumptions on the weight and the symbol we give a characterization of those weighted composition operators on the Frechet space of continuous functions on a locally compact, σ -compact, non-compact Hausdorff space which are generators of strongly continuous semigroups on these spaces.
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