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Proceedings of the American Mathematical Society

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

 

 

Multipliers on dual $ A\sp*$-algebras


Author: B. J. Tomiuk
Journal: Proc. Amer. Math. Soc. 62 (1977), 259-265
MSC: Primary 46K99; Secondary 46M05
MathSciNet review: 0433215
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Abstract: Let A be an $ {A^\ast}$-algebra which is a dense $ ^\ast$-ideal of a $ {B^\ast}$-algebra $ \mathfrak{A}$. We use tensor products and the algebra $ {M_l}(A)$ of left multipliers on A to obtain a characterization of duality in A. We show, moreover, that if A is dual then $ {M_l}(A)$ is algebra isomorphic to the second conjugate space $ {\mathfrak{A}^{\ast \ast}}$ of $ \mathfrak{A}$ when $ {\mathfrak{A}^{\ast \ast}}$ is given Arens product.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0433215-4
Keywords: Dual $ {A^\ast}$-algebra, multipliers, Arens product, projective tensor product, Banach A-module
Article copyright: © Copyright 1977 American Mathematical Society