Invariant means and analytic actions
Theodore Mitchell · Pacific Journal of Mathematics · 1979
Let T X D->Dbe a separately continuous analytic action of a semitopological semigroup T on D, the open unit disk in the complex plane, and let K be a compact T-invariant subset of D. The chief result of this paper is that if AP(T), the space of almost periodic functions on T, has a left invariant mean, then D contains a common fixed-point of T. As a special case, we show that a finite group of analytic self maps of D has a common fixed-point in Ώ.