Invariant means and analytic actions

Theodore Mitchell

Vol. 85 (1979), No. 1, 145–153

DOI: 10.2140/pjm.1979.85.145

Abstract

Lel T ×D → D be 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 D.

Mathematical Subject Classification 2000

Primary: 43A07

Secondary: 22A20, 47H10

Milestones

Received: 21 September 1978

Published: 1 November 1979