A Representation Theorem for Archimedean Riesz Spaces

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 represen...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2024-06, Vol.21 (4), Article 141
Main Author: Wickstead, A. W.
Format: Article
Language:English
Subjects:
Homomorphisms
Mathematics
Mathematics and Statistics
Representations
Tensors
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Summary: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.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-024-02684-3