×

zbMATH — the first resource for mathematics

Blocks in pairwise summable generalized effect algebras. (English) Zbl 1310.81018
Summary: We study the so-called pairwise summable generalized effect algebras and show some conditions under which they are generalized MV-effect algebras. Moreover, we give a necessary and sufficient condition for finite antichains of elements in pairwise summable generalized effect algebras under which they are sets of atoms of sub-generalized effect algebras, which are generalized MV-effect algebras in their own right. Simultaneously, we give counterexamples which show properties of those antichains which are not necessary or sufficient to be atoms of such generalized MV-effect algebras.
MSC:
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
03G12 Quantum logic
06A06 Partial orders, general
06C15 Complemented lattices, orthocomplemented lattices and posets
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Blank, J.; Exner, P.; Havlíček, M., Hilbert Space Operators in Quantum Physics, (2008), Springer Berlin · Zbl 1163.47060
[2] Dvurečenskij, A.; Pulmannová, S., New Trends in Quantum Structures, (2000), Kluwer Acad. Publ., Dordrecht/Ister Science Bratislava · Zbl 0987.81005
[3] Foulis, D. J.; Bennett, M. K., Effect algebras and unsharp quantum logics, Found. Phys., 24, 1331-1352, (1994) · Zbl 1213.06004
[4] Goodearl, K., Partially Ordered Abelian Groups with Interpolation, (1985), A.M.S. Math. Surveys and Monographs No. 20 Providence
[5] Hedlíková, J.; Pulmannová, S., Generalized difference posets and orthoalgebras, Acta Math. Univ. Comenianae, XLV, 247-279, (1996) · Zbl 0922.06002
[6] J. janda and Z. extensions of ordering sets of states from effect algebras onto their macneille completions riečanová:, Inter. J. Theor. Phys., 52, 6, 2171-2180, (2013) · Zbl 1270.06005
[7] Kalmbach, G.; Riečanová, Z., An axiomatization for abelian relative inverses, Demonstratio Math., 27, 769-780, (1994) · Zbl 0826.08002
[8] Kôpka, F., Compatiblity in D-posets, Inter. J. Theor. Phys., 34, 1525-1531, (1995) · Zbl 0843.03042
[9] Kôpka, F.; D-posets Chovanec, F., Math. Slovaca, 44, 21-34, (1994)
[10] Paseka, J.; Riečanová, Z., Inherited properties of effect algebras preserved by isomorphisms, Acta Polytechnica, 53, 3, 308-313, (2013)
[11] Riečanová, Z., Basic decomposition of elements and Jauch-piron effect algebras, Fuzzy Sets Syst., 155, 1, 138-149, (2005) · Zbl 1073.81014
[12] Riečanová, Z., Subalgebras, intervals and central elements of generalized effect algebras, Inter. J. Theor. Phys., 38, 3209-3220, (1999) · Zbl 0963.03087
[13] Riečanová, Z., Generalization of blocks for D-lattices and lattice-ordered effect algebras, Inter. J. Theor. Phys., 39, 2, 231-237, (2000) · Zbl 0968.81003
[14] Riečanová, Z.; Janda, J., Maximal subsets of pairwise summable elements in generalized effect algebras, Acta Polytechnica, 53, 5, 457-461, (2013)
[15] Z. riečanová and I. generalized homogenoeus, prelattice and mv-effect algebras marinová:, Kybernetika, 41, 2, 129-142, (2005)
[16] Riečanová, Z; Zajac, M., Hilbert space effect-representations of effect algebras, Rep. Math. Phys., 70, 2, 283-290, (2012) · Zbl 1268.81014
[17] Riečanová, Z.; Zajac, M.; Pulmannová, S., Effect algebras of positive linear operators densely defined on Hilbert spaces, Rep. Math. Phys., 68, 261-270, (2011) · Zbl 1250.81015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.