Multipliers and duality in $A\sp{\ast} $-algebras

Abstract

Let $A$ be an ${A^ \ast }$-algebra which is a dense $\ast$-ideal of a ${B^ \ast }$-algebra. Let ${M_r}(A)$ be the algebra of all bounded linear right multipliers on $A$. We obtain several characterizations of duality for $A$ in terms of the weak operator topology on ${M_r}(A)$ and the embedding of ${M_r}(A)$ into the conjugate space of a Banach space.