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Amenable groups for which very topologically left invariant mean is right invariant

Amenable groups for which very topologically left invariant mean is right invariant

Let G be an amenable locally compact group.A. L. T. Paterson proved that every topologically left invariant mean on L°°(G) is (*) (topologically) right invariant if and only if G has relatively compact conjugacy classes, provided G is discrete or compactly generated.He also conjectured that (*) holds for all amenable …