Adjoint Ergodic Theorems for Amenable Semigroups of Operators
Yōichi Kijima, Wataru Takahashi · Institutional Repositories DataBase (IRDB) · 1973
This theorem is very usefui in the ergodic theory of Markov proces66s.In this paper, we shall extend Lloyd's theorern to the case of an amenable semigroup by considering that the semigroup {T(t): O<t< oo} is commutative, The authors wish to express their hearty thanks to Professor Hisaharu Umegaki for many kind advices and suggestions in the course of preparing the present paper. Adjoint ergodic theorems.Let X be an abstract sernigroup and m(2) be the space of all bounded real valued functions of X with the supremum norm.An element ptEm(X)* (the dual space of m(X)) is mean on .S if ptt(e(t))=Il pt l[=1 where e(t)==1 for all tE2.A mean pt is left [right] z'nvariant'if pt,(A(t))= pt,(f<t)) [pt,(fS(t))=pt,(7C