Averaging theorems for linear operators in compact groups and semigroups
Volume 124 / 1997
Studia Mathematica 124 (1997), 249-258
DOI: 10.4064/sm-124-3-249-258
Abstract
The Weyl criterion for uniform distribution of a sequence has an especially simple form in compact abelian groups. The authors use this and the structure of compact monothetic groups and semigroups to generalise the convergence, under certain compactness conditions, of the operator averages: $n^{-1} ∑_{k=1}^n T^k → P (n→ ∞)$ where P is a projection associated with the eigenvalue one of T.
