Fe b 20 09 MODULE WEAK BANACH - SAKS AND MODULE SCHUR PROPERTIES OF HILBERT C ∗ - MODULES

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 studied. A number of useful characterizations of properties of Hilbert C∗-modules is obtained. In particular, some interrelations of these properties with the self-duality property of countably generated Hilbert C∗-modules are established.