SEMIGROUP ACTIONS , WEAK ALMOST PERIODICITY, AND INVARIANT MEANS
Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Ban...
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| Format: | Article |
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| Language: | English |
| Published: |
University of Tehran
1990-03-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Online Access: | https://jsciences.ut.ac.ir/article_31393_97dba61c61ae0f28f3f15144dcd3ab92.pdf |
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| Summary: | Let S be a topological semigroup acting on a topological space X. We
develop the theory of (weakly) almost periodic functions on X, with respect
to S, and form the (weakly) almost periodic compactifications of X and S,
with respect to each other. We then consider the notion of an action of Son a
Banach space, and on its dual, and after defining S-invariant means for such a
space, we give a result concerning the existence of such means, and apply it to
prove the existence of a G-invariant mean on the space of weakly almost
periodic functions defined on a topological space on which a topological
group G acts. |
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| ISSN: | 1016-1104 2345-6914 |