Maximal Subsets of Pairwise Summable Elements in Generalized Effect Algebras
| Authors | |
|---|---|
| Year of publication | 2013 |
| Type | Article in Periodical |
| Magazine / Source | Acta Polytechnica |
| MU Faculty or unit | |
| Citation | |
| Web | http://ojs.cvut.cz/ojs/index.php/ap/article/view/1865 |
| Doi | http://dx.doi.org/10.14311/AP.2013.53.0457 |
| Field | General mathematics |
| Keywords | (generalized) effect algebra; MV-effect algebra; summability block; compatibility block; linear operators in Hilbert spaces |
| Description | We show that in any generalized effect algebra (G;+,0) a maximal pairwise summable subset is a sub-generalized effect algebra of (G;+, 0), called a summability block. If G is lattice ordered, then every summability block in G is a generalized MV-effect algebra. Moreover, if every element of G has an infinite isotropic index, then G is covered by its summability blocks, which are generalized MV-effect algebras in the case that G is lattice ordered. We also present the relations between summability blocks and compatibility blocks of G. Counterexamples, to obtain the required contradictions in some cases, are given. |
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