Ergodic Theory and Probabilistic Approximations for Generalized Operator Semigroups

摘要

The definition of Abel-ergodic and Cesàro-ergodic about generalized operator semigroups are given and some characteristics of two ergodicities are discussed. Then the equivalence conditions of two ergodicities are obtained. At last, by means of the Pettis integral, the operator- valued mathematical expect and the generalized continuous modified modulus, the probabilistic approximation and convergent rates are given for generalized operator semigroups.