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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Arens product and the algebra of double multipliers


Author: Pak Ken Wong
Journal: Proc. Amer. Math. Soc. 94 (1985), 441-444
MSC: Primary 46H05
DOI: https://doi.org/10.1090/S0002-9939-1985-0787890-X
MathSciNet review: 787890
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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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DOI: https://doi.org/10.1090/S0002-9939-1985-0787890-X
Keywords: Arens product, Arens regularity, weak approximate identity, double multiplier, $ {B^ * }$-algebra, dual algebra
Article copyright: © Copyright 1985 American Mathematical Society