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On group actions with
nonzero fixed points
Joe W. Jenkins |
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Vol. 91 (1980), No. 2, 363–371
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Abstract |
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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
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Milestones
Received: 5 October 1979
Published: 1 December 1980
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Authors |
| Joe W. Jenkins | |
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