Extreme point properties of fixed-point sets
1972 ◽
Vol 6
(2)
◽
pp. 241-249
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Keyword(s):
We consider a semigroup S acting as affine continuous maps on a compact convex set X. F denotes the corresponding set of fixed points. Let exX and exF denote the corresponding sets of extreme points. If X is a simplex, conditions are given which ensure that when x ε F, the maximal measure representing x invariant under S. We also prove exF = F ∩ exX under conditions involving extreme amenability of S. Topological properties of exF are also studied.
2001 ◽
Vol 70
(3)
◽
pp. 323-336
◽
Keyword(s):
1988 ◽
Vol 37
(2)
◽
pp. 177-200
1987 ◽
Vol 35
(2)
◽
pp. 267-274
◽
1972 ◽
Vol 11
(4)
◽
pp. 385-392
◽
1997 ◽
Vol 125
(10)
◽
pp. 3075-3087
◽
1978 ◽
Vol 30
(03)
◽
pp. 449-454
◽