Arens regularity and derivations of Hilbert modules with the certain product

Let A be a C^*-algebra and E be a left Hilbert A-module. In this paper we define a product on E that making it into a Banach algebra and show that under the certain conditions E  is Arens regular. We also study the relationship between derivations of A and E.

Arens regularity and derivations of Hilbert modules with the certain product Keywords:

C^{*} , C^*-algebra , algebra , Hilbert C^*-module , Banach algebra , Hilbert C^{*} , Arens regular , module , Derivation