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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The order bidual of almost $f$-algebras and $d$-algebras
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by S. J. Bernau and C. B. Huijsmans PDF
Trans. Amer. Math. Soc. 347 (1995), 4259-4275 Request permission

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
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 4259-4275
  • MSC: Primary 46H05; Secondary 46A40, 46B42
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1308002-0
  • MathSciNet review: 1308002