Invariant means on almost periodic functions and equicontinuous actions

Author:
Anthony To Ming Lau

Journal:
Proc. Amer. Math. Soc. **49** (1975), 379-382

MSC:
Primary 43A07

DOI:
https://doi.org/10.1090/S0002-9939-1975-0367551-5

MathSciNet review:
0367551

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Abstract: Let be a topological semigroup such that the almost periodic functions on have a left invariant mean (this is the case, for example, when has finite intersection property for closed right ideals). Then whenever acts equicontinuously on a compact Hausdorff space , there exists a compact group of homeomorphisms acting equicontinuously on a retract of such that has a common fixed point in if and only if has a common fixed point in . This result generalises some recent work of T. Mitchell. As an application, we show that whenever acts equicontinuously on the closed unit interval , then contains a common fixed point for .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0367551-5

Keywords:
Invariant means,
almost periodic functions,
compact groups,
topological semigroups,
equicontinuous mappings,
common fixed points,
commuting real functions

Article copyright:
© Copyright 1975
American Mathematical Society