Nets of extreme Banach limits

Author:
Rodney Nillsen

Journal:
Proc. Amer. Math. Soc. **55** (1976), 347-352

MSC:
Primary 43A07

DOI:
https://doi.org/10.1090/S0002-9939-1976-0407530-3

MathSciNet review:
0407530

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the set of natural numbers and let be an injection having no periodic points. Let be the set of -invariant means on . When let , where the supremum is taken over all . It is shown that when , there is a sequence of extreme points of which has no extreme weak limit points and such that for . As a consequence, the extreme points of are not weak compact.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1976-0407530-3

Keywords:
Motions,
means,
invariant means,
Banach limits,
extreme points,
ergodic measure,
Stone-Čech compactification

Article copyright:
© Copyright 1976
American Mathematical Society