Remarks on actions on compacta by some infinite-dimensional groups

Details Remarks on actions on compacta by some infinite-dimensional groups Remarks on actions on compacta by some infinite-dimensional groups

2002-04-16

arxiv.org/abs/math/0204202v2

in: Infinite-Dimensional Lie Groups in Geometry and Representation Theory (Washington, D.C., 2000), World Sci. Publishing, Riv

Mathematics

Dynamical Systems

19 pages, LaTeX with World Scientific macros, to appear in Proc. Conf. on Infinite-Dimensional Lie Groups in Geometry and Repr

Scientific paper

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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