Remarks on actions on compacta by some infinite-dimensional groups

Vladimir Pestov

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Remarks on actions on compacta by some infinite-dimensional groups

Vladimir Pestov

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Abstract

We discuss some techniques related to equivariant compactifications of uniform spaces and amenability of topological groups. In particular, we give a new proof of a recent result by Glasner and Weiss describing the universal minimal flow of the infinite symmetric group ${\mathfrak S}_\infty$ with the standard Polish topology, and extend Bekka's concept of an amenable representation, enabling one to deduce non-amenability of the Banach--Lie groups $\GL(L_p)$ and $\GL(\ell_p)$, $1\leq p <\infty$.

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BibTeX RIS

Vladimir Pestov. 2002-04-23. Remarks on actions on compacta by some infinite-dimensional groups. https://arxiv.org/abs/math/0204202

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