Remarks on actions on compacta by some infinite-dimensional groups
Abstract
Description
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 $\GL(\ell_p)$, $1\leq p <\infty$.
19 pages, LaTeX with World Scientific macros, to appear in Proc. Conf. on Infinite-Dimensional Lie Groups in Geometry and Representation Theory (Howard Univ., Washington, D.C., August 2000)
19 pages, LaTeX with World Scientific macros, to appear in Proc. Conf. on Infinite-Dimensional Lie Groups in Geometry and Representation Theory (Howard Univ., Washington, D.C., August 2000)