Maximal Subsets of Pairwise Summable Elements in Generalized Effect Algebras

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Authors	RIEČANOVÁ Zdenka JANDA Jiří
Year of publication	2013
Type	Article in Periodical
Magazine / Source	Acta Polytechnica
MU Faculty or unit	Faculty of Science
Citation
web	http://ojs.cvut.cz/ojs/index.php/ap/article/view/1865
Doi	https://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.
Related projects:	Mathematical structures and their physical applications