AMENABLE ACTIONS, INVARIANT MEANS AND BOUNDED COHOMOLOGY
نویسندگان
چکیده
منابع مشابه
Amenable Actions, Invariant Means and Bounded Cohomology
We show that topological amenability of an action of a countable discrete group on a compact space is equivalent to the existence of an invariant mean for the action. We prove also that this is equivalent to vanishing of bounded cohomology for a class of Banach G-modules associated to the action, as well as to vanishing of a specific cohomology class. In the case when the compact space is a poi...
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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...
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We study actions of countable discrete groups which are amenable in the sense that there exists a mean on X which is invariant under the action of G. Assuming that G is nonamenable, we obtain structural results for the stabilizer subgroups of amenable actions which allow us to relate the first `-Betti number of G with that of the stabilizer subgroups. An analogous relationship is also shown to ...
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ژورنال
عنوان ژورنال: Journal of Topology and Analysis
سال: 2012
ISSN: 1793-5253,1793-7167
DOI: 10.1142/s1793525312500161