Remarks on actions on compacta by some infinite-dimensional groups

Vladimir Pestov

Remarks on actions on compacta by some infinite-dimensional groups

Dynamical Systems 2007-09-03 v2

Authors: Vladimir Pestov

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 $\GL(\ell_p)$ , $1\leq p <\infty$ .

Keywords

amenable groups descriptive set theory lie groups

Cite

@article{arxiv.math/0204202,
  title  = {Remarks on actions on compacta by some infinite-dimensional groups},
  author = {Vladimir Pestov},
  journal= {arXiv preprint arXiv:math/0204202},
  year   = {2007}
}

Comments

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)

Remarks on actions on compacta by some infinite-dimensional groups

Abstract

Keywords

Cite

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