Characterization of Riesz Spaces with Topologically Full Center

Alpay, Safak
Orhon, Mehmet
Let E be a Riesz space and let E-similar to denote its order dual. The orthomorphisms Orth(E) on E, and the ideal center Z(E) of E, are naturally embedded in Orth(E-similar to) and Z(E-similar to) respectively. We construct two unital algebra and order- continuous Riesz homomorphisms.


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A Riesz space E is said to have b-property if each subset which is order bounded in E(similar to similar to) is order bounded in E. The relationship between b-property and completeness, being a retract and the absolute weak topology vertical bar sigma vertical bar (E(similar to), E) is studied. Perfect Riesz spaces are characterized in terms of b-property. It is shown that b-property coincides with the Levi property in Dedekind complete Frechet lattices.
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Citation Formats
S. Alpay and M. Orhon, “Characterization of Riesz Spaces with Topologically Full Center,” 2013, p. 35, Accessed: 00, 2020. [Online]. Available: