Smearings of States Defined on Sharp Elements Onto Effect Algebras |
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Authors: | Zdenka Riečanová |
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Affiliation: | (1) Department of Mathematics, Faculty of Electrical Engineering and Information Technology, STU, Ilkoviova 3, 812 19 Bratislava 1, Slovak Republic |
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Abstract: | In some sense, a lattice effect algebra E is a smeared orthomodular lattice S(E), which then becomes the set of all sharp elements of the effect algebra E. We show that if E is complete, atomic, and (o)-continuous, then a state on E exists iff there exists a state on S(E). Further, it is shown that such an effect algebra E is an algebraic lattice compactly generated by finite elements of E. Moreover, every element of E has a unique basic decomposition into a sum of a sharp element and a -orthogonal set of unsharp multiples of atoms. |
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Keywords: | effect algebra state sharp elements order-continuity |
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