2020/05/16 by Ali Jabbari, Jabbari, Ali, Ebadian, Ali +3
Economics, Econometrics and Finance · Mathematics · #22A20 #22D15 #43A07 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Advanced Topology and Set Theory #Economic theories and models #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2005.08089
openalex publication_date 2020/05/16 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this paper, we introduce a weak form of amenability on topological\nsemigroups that we call \φ-amenability, where \φ is a character\non a topological semigroup. Some basic properties of this new notion are\nobtained and by giving some examples, we show that this definition is weaker\nthan the amenability of semigroups. As a noticeable result, for a topological\nsemigroup S, it is shown that if S is \φ-amenable, then S is\namenable. Moreover, \φ-ergodicity for a topological semigroup S is\nintroduced and it is proved that under some conditions on S and a Banach\nspace X, \φ-amenability and \φ-ergodicity of any\nantirepresntation defined by a right action S on X, are equivalent. A\nrelation between \φ-amenability of topological semigroups and existance\nof a common fixed point is investigated and by this relation, Hahn-Banach\nproperty of topological semigroups in the sense of \φ-amenability\ndefined and studied.\n