Schauder's fixed point and amenability of a group
Keywords
Amenable groups, fixed points, invariant measuresAbstract
A criterion for existence of a fixed point for an affine action of a given group on a compact convex space is presented. From this we derive that a discrete countable group is amenable if and only if there exists an invariant probability measure for any action of the group on a Hilbert cube. Amenable properties of the group of all isometries of the Urysohn universal homogeneous metric space are also discussed.Downloads
Published
2007-06-01
How to Cite
1.
BOGATYI, Semeon A. and FEDORCHUK, Vitaly V. Schauder’s fixed point and amenability of a group. Topological Methods in Nonlinear Analysis. Online. 1 June 2007. Vol. 29, no. 2, pp. 383 - 401. [Accessed 29 March 2024].
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