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
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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