## Matthias Neufang, Jan Pachl, Juris Steprāns, Group actions whose space of invariant means is finite dimensional

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Volume 1, Issue 3, 1 December 2017, Pages 307-319

Abstract. It is shown that under various set theoretic hypotheses there is an amenable subgroup $F$ of the full symmetric group on $\mathbb{N}$ such that the space of means on $\mathbb{N}$ invariant under the natural action of $F$ is finite dimensional, yet the Arens multiplication by invariant means in $l_{\infty}^*(F)$ is never weak* to weak* continuous.