Topologically ergodic C0-semigroups and ergodicity of their operators

Abstract

This paper introduces topologically ergodic C0-semigroups. It demonstrates that the set of topologically ergodic C0-semigroups is a proper subset of the set of recurrent C0-semigroups. It also proves that these C0-semigroups exist in any innite-dimensional space. In addition, the article establishes that the topological ergodicity of any operator of a C0-semigroup implies the topological ergodicity of the C0-semigroup and vice versa. Moreover, the research shows that the topological ergodicity of a C0-semigroup is equivalent to the topological ergodicity of the direct sum of the C0-semigroup with itself. Lastly, the research states some criteria for topological ergodicity which are in accordance with open sets and generalized kernels.