Continuing the research on the Banach-Saks and Schur properties started in (cf. [10]) we investigate analogous properties in the module context. As an environment serves the class of Hilbert C∗-modules. Some properties of weak module topologies on Hilbert C∗-modules are described. Natural module analogues of the classical weak Banach-Saks and the classical Schur properties are defined and studi...

in this paper, we extend some propositions of banachalgebras into module actions and establish the relationships betweentopological centers of module actions. we introduce some newconcepts as                         -property and -property for banach modules and obtain some conclusions inthe topological center of module actions and arens regularity of banachalgebras.