科研之友
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摘要
Under suitable conditions, a measurable action of a semigroup S on a probability space generates various sigma-fields reflecting the dynamical properties of the associated representation of S and containing the information provided by certain subspaces of determined by the representation. For example, the functions in with norm relatively compact orbits under S are precisely the functions that are measurable with respect to the sigma-field of almost periodic events. In the special case of a measure-preserving action, the minimal projection operator associated with the action is a conditional expectation with respect to this sigma-field, leading to a result on transformation of martingales. The unifying construct throughout the paper is the weakly almost periodic compactification of S, a powerful tool that provides a convenient platform to study operator semigroups associated with the action.
- 出版日期2014-2
