A CERTAIN CLASS OF ARENS REGULAR BILINEAR MAPPINGS

In this paper we extend the notion of quasi-multipliers to the dual of a Banach algebra A which seconddual has a mixed identity. We consider algebras satisfying weaker condition than Arens regularity. Amongothers we study the relation between arens regularity of a quasi-multiplier m : A A ! A and the Banachalgebra A. We also show that if A is Arens regular then the algebra QMr(A) of all bilinear and separatelycontinuous right quasi-multipliers of A∗ is Arens regular