Abstract
It is shown that the order bidual X ~~ of an Archimedean semiprime f -algebra X has a unit element for the Arens multiplication if and only if every positive linear functional on X extends to a positive linear functional on the f -algebra Orth (X) of all orthomorphisms on X.
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Boulabiar, K., Jaber, J. The order bidual of f -algebras revisited. Positivity 15, 271–279 (2011). https://doi.org/10.1007/s11117-010-0072-x
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DOI: https://doi.org/10.1007/s11117-010-0072-x
Keywords
- Arens multiplication
- Extension
- f -algebra
- Order dual
- Order bidual
- Orthomorphism
- Semiprime
- Positive linear functional
- Riesz space