Spectral and ergodic properties of the analytic generators

Abstract

In this paper similarity situations between one-parameter groups of operators are characterized in terms of analytic generators and spectral subspaces, and ergodic properties of one-parameter groups are studied. These topics permit us to give “noncommutative” extensions of classical results from the theory of Hardy's Hp spaces. As major applications we mention the possibility of use of the analyticity notion from Arveson (Amer. J. Math.89 (1967), 578–642) for one-parameter groups of *-automorphisms of operator algebras with “good” ergodic properties (see Section 3), and a procedure to “improve” implementing groups of unitaries for one-parameter groups of *-automorphisms of operator algebras (see Section 5).