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Continuous invariant averagings. (English) Zbl 1277.43003
Main results: For every equicontinuous almost periodic linear representation of a group in a complete locally convex space $$L$$ with the countability property, there exists a unique invariant averaging; it is continuous and is expressed by using the $$L$$-valued invariant mean of Bochner and von Neumann. An analog of Wiener’s approximation theorem for an equicontinuous almost periodic linear representation in a locally convex space with the countability property is proved.
##### MSC:
 43A07 Means on groups, semigroups, etc.; amenable groups 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions 16W22 Actions of groups and semigroups; invariant theory (associative rings and algebras)
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