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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Topological invariant means on locally compact groups and fixed points.


Author: James C. S. Wong
Journal: Proc. Amer. Math. Soc. 27 (1971), 572-578
MSC: Primary 22.65
MathSciNet review: 0272954
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Abstract: A locally compact group $ G$ is said to have the fixed point property if whenever $ G$ acts affinely on a compact convex subset $ S$ of a separated locally convex space $ E$ with the map $ G \times S \to S$ jointly continuous, there is a fixed point for the action. N. Rickert has proved that $ G$ has this fixed point property if $ G$ is amenable. In this paper, we study the fixed point property for actions of the algebras $ {L_1}(G)$ and $ M(G)$ and prove some fixed point theorems for locally compact groups.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0272954-X
PII: S 0002-9939(1971)0272954-X
Keywords: Locally compact groups, fixed point properties, fixed point theorems, amenability, topological left introverted spaces, convolution algebras $ {L_1}(G)$ and $ M(G)$, Silverman's invariant extension property
Article copyright: © Copyright 1971 American Mathematical Society