| Title: | REMARKS ON ACTIONS ON COMPACTA BY SOME INFINITE-DIMENSIONAL GROUPS |
| Source: | INFINITE DIMENSIONAL LIE GROUPS IN GEOMETRY AND REPRESENTATION THEORY (pp 145-163)
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| Author(s): | VLADIMIR PESTOV
http://www.mcs.vuw.ac.nz/~vova
New permanent address beginning July 1, 2002: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, K1N 6N5, Canada.
School of Mathematical and Computing Sciences, Victoria University of Wellington, P. O. Box 600, Wellington, New Zealand
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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  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(Lp) and GL(ℓp), 1 ≤ p < ∞. |
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