Vol. 91, No. 2, 1980

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On group actions with nonzero fixed points

Joe W. Jenkins

Vol. 91 (1980), No. 2, 363–371

Let G be a locally compact group that acts continuously by linear transformations on a locally convex space E and let K be a compact convex subset of E that is invariant under this action. In order to conclude that K has a nonzero fixed point, it is necessary that both G and K satisfy certain conditions. With these assumptions on K, it is shown that the existence of nonzero fixed points is equivalent to polynomial growth on G, provided G is connected or discrete, finitely generated and solvable.

Mathematical Subject Classification 2000
Primary: 22D05
Received: 5 October 1979
Published: 1 December 1980
Joe W. Jenkins