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Extreme point properties of fixed-point sets

Published online by Cambridge University Press:  17 April 2009

Rodney Nillsen
Rodney Nillsen
Affiliation:
Flinders University of South Australia, Bedford Park, South Australia The Royal University of Malta, Msida, Malta.
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 2 , April 1972 , pp. 241 - 249
Copyright
Copyright © Australian Mathematical Society 1972

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