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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the Arens product and annihilator algebras


Author: Pak-ken Wong
Journal: Proc. Amer. Math. Soc. 30 (1971), 79-83
MSC: Primary 46.50
MathSciNet review: 0281005
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Abstract: The purpose of this paper is to generalize two results in a recent paper by B. J. Tomiuk and the author. Let A be a $ {B^ \ast }$-algebra and $ M(A)$ the algebra of double centralizers of A. We show that A is a dual algebra if and only if $ M(A)$ coincides with $ {A^{ \ast\ast }}$. We also obtain that if A is an annihilator $ {A^\ast}$-algebra, then $ {\pi _A}(A)$ is a two-sided ideal of $ {A^{ \ast \ast }}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0281005-2
PII: S 0002-9939(1971)0281005-2
Keywords: Dual $ {B^ \ast }$-algebra, Arens product, double centralizer, annihilator algebra, minimal idempotent, group algebra of a compact group
Article copyright: © Copyright 1971 American Mathematical Society