Fixed Points For Bounded Orbits In Hilbert Spaces

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 a-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.


Published in:
Annales Scientifiques De L Ecole Normale Superieure, 50, 1, 131-156
Year:
2017
Publisher:
Paris, Elsevier
ISSN:
0012-9593
Laboratories:




 Record created 2017-05-01, last modified 2018-01-28

External links:
Download fulltextURL
Download fulltextPreprint
Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)