Arens product and the algebra of double multipliers

Wong, Pak Ken

doi:10.1090/S0002-9939-1985-0787890-X

Arens product and the algebra of double multipliers
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Proc. Amer. Math. Soc. 94 (1985), 441-444 Request permission

Abstract:

Let $A$ be a semisimple Banach algebra and $M(A)$ the algebra of double multipliers of $A$. We show that $M(A)$ is isomorphic to $({A^{ * * }}, \circ )$ if and only if $A$ has the following properties: (1) $A$ is Arens regular, (2) $A$ has a weak approximate identity, and (3) $\pi (A)$ is an ideal of $({A^{ * * }}, \circ )$.

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