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

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### 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 Fr\'echet space of continuous functions on a locally compact, $$\sigma$$-compact, non-compact Hausdorff space which are generators of strongly continuous semigroups on these spaces.

### Most cited references8

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### Surjectivity of differential operators and linear topological invariants for spaces of zero solutions

(2019)
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### Strongly continuous semigroups on some Fréchet spaces

(2014)
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### A note on mean ergodic composition operators on spaces of holomorphic functions

(2011)
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### Author and article information

###### Journal
23 July 2018
###### Article
1807.08557