Resumen de A weak form of amenability of topological semigroups and its applications in ergodic and fixed point theories

Ali Ebadian, Ali Jabbari, Madjid Eshaghi Gordji

• In this paper, we introduce a weak form of amenability on topological semigroups that we call φ-amenability, where φ is a character on a topological semigroup. Some basic properties of this new notion are obtained and by giving some examples, we show that this definition is weaker than the amenability of semigroups. As a noticeable result, for a topological semigroup S, it is shown that if S is φ-amenable, then S is amenable. Moreover, φ-ergodicity for a topological semigroup S is introduced and it is proved that under some conditions on S and a Banach space X, φ-amenability and φ-ergodicity of any antirepresntation defined by a right action S on X, are equivalent. A relation between φ-amenability of topological semigroups and the existence of a common fixed point is investigated and by this relation, Hahn-Banach property of topological semigroups in the sense of φ-amenability defined and studied.