On the ergodic theory of contractions

Abstract

We give a formulation of the ergodic theory of Banach space contractions which has as a special case Sine's finite dimension criterion for C(X). For Grothendieck spaces, a sharper condition for ergodicity of an operotor is given, and a known mean divergence theorem for G-spaces of type C(X) is shown to hold (in su itable form) for any G-space. Finally we show that for G-spaces ergodicity of T is closely related to that of the adjoint T*.