A Note on the Equivariant Coarse Embedding into Hilbert Spaces
Several equivalent formulations are given for equivariant coarse embedding into Hilbert space.Using these equivalent definitions,it is proved that for a metric space X and a Hilbert space H with proper and isometric group actions on both of them,if X is coarsely embeddable into H and the group is amenable,then the coarse embedding can be modified to be equivariant by using the invariant mean property of the amenable group.
equivariant coarse emdeddingproper and isometric group actionamenable groups
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