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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A representation of sup-completion
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by Achintya Raya Polavarapu and Vladimir G. Troitsky;
Proc. Amer. Math. Soc. 152 (2024), 3403-3411
DOI: https://doi.org/10.1090/proc/16796
Published electronically: June 5, 2024

Abstract:

It was showed by Donner in [Extension of positive operators and Korovkin theorems, Lecture Notes in Mathematics, vol. 904, Springer-Verlag, Berlin-New York, 1982] that every order complete vector lattice $X$ may be embedded into a cone $X^s$, called the sup-completion of $X$. We show that if one represents the universal completion of $X$ as $C^\infty (K)$, then $X^s$ is the set of all continuous functions from $K$ to $[-\infty ,\infty ]$ that dominate some element of $X$. This provides a functional representation of $X^s$, as well as an easy alternative proof of its existence.
References
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Bibliographic Information
  • Achintya Raya Polavarapu
  • Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada
  • Email: polavara@ualberta.ca
  • Vladimir G. Troitsky
  • Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada
  • MR Author ID: 341818
  • Email: troitsky@ualberta.ca
  • Received by editor(s): June 8, 2023
  • Received by editor(s) in revised form: November 14, 2023, and January 14, 2024
  • Published electronically: June 5, 2024
  • Additional Notes: The second author was supported by an NSERC grant.
  • Communicated by: Stephen Dilworth
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 3403-3411
  • MSC (2020): Primary 46A40
  • DOI: https://doi.org/10.1090/proc/16796
  • MathSciNet review: 4767271