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Quasi-multipliers of the dual of a Banach algebra. (English) Zbl 1222.47058
Summary: In this paper, we extend the notion of quasi-multipliers to the dual of a Banach algebra $A$ whose second dual has a mixed identity. We consider algebras satisfying weaker conditions than Arens regularity. Among other things, we prove that, for an Arens regular Banach algebra which has a bounded approximate identity, the space $QM_r(A^\ast)$ of all bilinear and separately continuous right quasi-multipliers of $A^\ast$ is isometrically isomorphic to $A^{\ast \ast}$. We discuss the strict topology on $QM_r(A^\ast)$ and apply our results to $C^\ast$-algebras and to the group algebra of a compact group.
47B48Operators on Banach algebras
46H25Normed modules and Banach modules, topological modules
Full Text: EMIS