Power bounded weighted composition operators on function spaces defined by local properties

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-degenrate parabolic operators. Moreover, under mild assumptions on the weight and the symbol we give a characterisation of those weighted composition operators on the Fréchet space of continuous functions on a locally compact, $\sigma$-compact, non-compact Hausdorff space which are generators of strongly continuous semigroups on these spaces.

arXiv commentv2: accepted manuscript; 27 pages

References in corpus (2)

• Dynamics of weighted composition operators on function spaces defined by local properties
• Non power bounded generators of strongly continuous semigroups

Cited by in corpus (7)

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• Topologizable and power bounded weighted composition operators on spaces of distributions
• Mean ergodic composition operators on spaces of smooth functions and distributions
• An approximation theorem of Runge type for kernels of certain non-elliptic partial differential operators
• Lower bounds on $L^p$ quasi-norms and the Uniform Sublevel Set Problem
• On a new type of Inequality related to the Uniform Sublevel Set Problem