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

Arens regularity of certain Banach algebras which are ideals of a Banach algebra


Author: Sheila A. McKilligan
Journal: Proc. Amer. Math. Soc. 50 (1975), 223-229
MSC: Primary 46H20
MathSciNet review: 0372617
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Abstract: The question of Arens regularity for a dual $ {A^ \ast }$-algebra which is a dense two-sided ideal of a $ {B^ \ast }$-algebra has been discussed by Wong and by Alexander. We consider the Arens regularity of some Banach algebras which are dense ideals of Arens regular Banach algebras to prove, among other results, that any commutative $ {A^ \ast }$-algebra which is an ideal of its completion in the auxiliary norm is Arens regular.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0372617-X
PII: S 0002-9939(1975)0372617-X
Keywords: Arens regular, $ {A^ \ast }$-algebra
Article copyright: © Copyright 1975 American Mathematical Society