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- W2046237573 abstract "Recently Lau [15] generalized a result of Yeadon [25]. In the present paper we generalize Yeadon's result in another direction recasting it as a theorem of ergodic type. We call the notion of ergodicity required left mean-ergodicity and show how it relates to the mean-ergodicity of Nagel [21]. Connections with the existence of invariant means on spaces of continuous functions on semitopological semigroups S are made, connections concerning, among other things, a fixed point theorem of Mitchell [20] and Schwartz's property P of W ∗ -algebras [22]. For example, if M ( S ) is a certain subspace of C ( S ) (which was considered by Mitchell and is of almost periodic type, i.e., the right translates of a member of M ( S ) satisfy a compactness condition), then the assumption that M ( S ) has a left invariant mean is equivalent to the assumption that every representation of S of a certain kind by operators on a linear topological space X is left mean-ergodic. An analog involving the existence of a (left and right) invariant mean on M ( S ) is given, and we show our methods restrict in the Banach space setting to give short direct proofs of some results in [4], results involving the existence of an invariant mean on the weakly almost periodic functions on S or on the almost periodic functions on S . An ergodic theorem of Lloyd [16] is generalized, and a number of examples are presented." @default.
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- W2046237573 date "1978-08-01" @default.
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- W2046237573 title "Left mean-ergodicity, fixed points, and invariant means" @default.
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- W2046237573 doi "https://doi.org/10.1016/0022-247x(78)90199-3" @default.
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