Topological invariant means on locally compact groups and fixed points.

Wong, James C. S.

doi:10.1090/S0002-9939-1971-0272954-X

Topological invariant means on locally compact groups and fixed points.
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by James C. S. Wong PDF

Proc. Amer. Math. Soc. 27 (1971), 572-578 Request permission

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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