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


Author: Bohdan J. Tomiuk
Journal: Proc. Amer. Math. Soc. 50 (1975), 281-288
MSC: Primary 46K15
DOI: https://doi.org/10.1090/S0002-9939-1975-0372627-2
MathSciNet review: 0372627
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0372627-2
Keywords: Dual $ {A^ \ast }$-algebra, multiplier, Arens product, weak operator topology
Article copyright: © Copyright 1975 American Mathematical Society

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