Lattice effect algebras with (o)-continuous faithful valuations
Effect algebras have been introduced by \textit{D. J. Foulis} and \textit{M. K. Bennett} [``Effect algebras and unsharp quantum logics'', Found. Phys. 24, 1331-1352 (1994)] to study quantum effects which may be unsharp. The main result of this paper goes as follows: Theorem 5.4. Let there exist an (o)-continuous faithful valuation on a lattice effect algebra \((E;\oplus,0,1)\). Then (i) \(E\) is modular, separable and (o)-continuous; (ii) \(E\) can be supremum and infimum densely embedded into a complete modular, separable and (o)-continuous effect algebra \(\widehat E\); (iii) there is a unique (o)-continuous faithful valuation \(\widehat\omega\) on \(\widehat E\) which extends \(\omega\).
scientific article; zbMATH DE number 1743109
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