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Fixed points for bounded orbits in Hilbert spaces | | Maxime Gheysens
; Nicolas Monod
; | | Date: |
3 Aug 2015 | | Abstract: | Consider the following property of a topological group G: every continuous
affine G-action on a Hilbert space with a bounded orbit has a fixed point. We
prove that this property characterizes amenability for locally compact
sigma-compact groups (e.g. countable groups). Along the way, we introduce a
"moderate" variant of the classical induction of representations and we
generalize the Gaboriau--Lyons theorem to prove that any non-amenable locally
compact group admits a probabilistic variant of discrete free subgroups. This
leads to the "measure-theoretic solution" to the von Neumann problem for
locally compact groups. We illustrate the latter result by giving a partial
answer to the Dixmier problem for locally compact groups. | | Source: | arXiv, 1508.0423 | | Services: | Forum | Review | PDF | Favorites | |
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