8 research outputs found
Modularity, Atomicity and States in Archimedean Lattice Effect Algebras
Effect algebras are a generalization of many structures which arise in
quantum physics and in mathematical economics. We show that, in every modular
Archimedean atomic lattice effect algebra that is not an orthomodular
lattice there exists an -continuous state on , which is
subadditive. Moreover, we show properties of finite and compact elements of
such lattice effect algebras
Two-valued states on Baer -semigroups
In this paper we develop an algebraic framework that allows us to extend
families of two-valued states on orthomodular lattices to Baer -semigroups.
We apply this general approach to study the full class of two-valued states and
the subclass of Jauch-Piron two-valued states on Baer -semigroups.Comment: Reports on mathematical physics (accepted 2013
Atomicity of lattice effect algebras and their sub-lattice effect algebras
summary:We show some families of lattice effect algebras (a common generalization of orthomodular lattices and MV-effect algebras) each element E of which has atomic center C(E) or the subset S(E) of all sharp elements, resp. the center of compatibility B(E) or every block M of E. The atomicity of E or its sub-lattice effect algebras C(E), S(E), B(E) and blocks M of E is very useful equipment for the investigations of its algebraic and topological properties, the existence or smearing of states on E, questions about isomorphisms and so. Namely we touch the families of complete lattice effect algebras, or lattice effect algebras with finitely many blocks, or complete atomic lattice effect algebra E with Hausdorff interval topology
Equational characterization for two-valued states in orthomodular quantum systems
In this paper we develop an algebraic framework in which several classes of two-valued states over orthomodular lattices may be equationally characterized. The class of two-valued states and the subclass of Jauch–Piron two-valued states are among the classes which we study.Fil: Domenech, Graciela. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Freytes Solari, Hector Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaFil: de Ronde, Christian. Center Leo Apostel; Bélgica. Vrije Unviversiteit Brussel; Bélgic
Modularity, Atomicity and States in Archimedean Lattice Effect Algebras
Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra E that is not an orthomodular lattice there exists an (o)-continuous state ω on E, which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras