A representation theorem for Archimedean Riesz spaces

A. W. Wickstead*

*Corresponding author for this work

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Abstract

In previous works, Buskes and the author have made use of representations of Archimedean Riesz spaces in terms of real-valued continuous functions defined on dense open subsets of a topological space in studying tensor products. These representations may be obtained from the Ogasawara–Maeda representation by means of restriction to the set on which representing functions are real-valued, rather than infinite. In this note, we show how to obtain such a representation as a simple consequence of the Krein–Kakutani representation of an order unit space. We conclude by studying the representation of Riesz homomorphisms in this setting.

Original languageEnglish
Article number141
Number of pages11
JournalMediterranean Journal of Mathematics
Volume21
Issue number4
DOIs
Publication statusPublished - Jun 2024

Keywords

  • 06F20
  • Archimedean Riesz spaces
  • representations

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