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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The order bidual of almost $ f$-algebras and $ d$-algebras


Authors: S. J. Bernau and C. B. Huijsmans
Journal: Trans. Amer. Math. Soc. 347 (1995), 4259-4275
MSC: Primary 46H05; Secondary 46A40, 46B42
MathSciNet review: 1308002
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Abstract: It is shown in this paper that the second order dual $ A''$ of an Archimedean (almost) $ f$-algebra $ A$, equipped with the Arens multiplication, is again an (almost) $ f$-algebra. Also, the order continuous bidual $ (A')_n'$ of an Archimedean $ d$-algebra $ A$ is a $ d$-algebra. Moreover, if the $ d$-algebra $ A$ is commutative or has positive squares, then $ A''$ is again a $ d$-algebra.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1308002-0
PII: S 0002-9947(1995)1308002-0
Keywords: Arens multiplication, $ f$-algebra, almost $ f$-algebra, $ d$-algebra, second order dual, bidual, order continuous bidual
Article copyright: © Copyright 1995 American Mathematical Society