12 found
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  1.  89
    Effect Algebras with the Riesz Decomposition Property and AF C*-Algebras.Sylvia Pulmannova - 1999 - Foundations of Physics 29 (9):1389-1401.
    Relations between effect algebras with Riesz decomposition properties and AF C*-algebras are studied. The well-known one-one correspondence between countable MV-algebras and unital AF C*-algebras whose Murray-von Neumann order is a lattice is extended to any unital AF C* algebras and some more general effect algebras having the Riesz decomposition property. One-one correspondence between tracial states on AF C*-algebras and states on the corresponding effect algebras is proved. In particular, pure (faithful) tracial states correspond to extremal (faithful) states on corresponding effect (...)
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  2.  85
    Hidden Variables and Bell Inequalities on Quantum Logics.Sylvia Pulmannová - 2002 - Foundations of Physics 32 (2):193-216.
    In the quantum logic approach, Bell inequalities in the sense of Pitowski are related with quasi hidden variables in the sense of Deliyannis. Some properties of hidden variables on effect algebras are discussed.
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  3.  35
    Characterizations of Commutative POV Measures.Anna Jenčová & Sylvia Pulmannová - 2009 - Foundations of Physics 39 (6):613-624.
    Two different characterizations of POV measures with commutative range are compared using a representation of some stochastic operators by (weak) Markov kernels. A representation by Choquet theorem is obtained as an integral over functions of a sharp observable appearing in one of the characterizations. A Naimark extension is constructed.
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  4.  22
    Type-Decomposition of an Effect Algebra.David J. Foulis & Sylvia Pulmannová - 2010 - Foundations of Physics 40 (9-10):1543-1565.
    Effect algebras (EAs), play a significant role in quantum logic, are featured in the theory of partially ordered Abelian groups, and generalize orthoalgebras, MV-algebras, orthomodular posets, orthomodular lattices, modular ortholattices, and boolean algebras.We study centrally orthocomplete effect algebras (COEAs), i.e., EAs satisfying the condition that every family of elements that is dominated by an orthogonal family of central elements has a supremum. For COEAs, we introduce a general notion of decomposition into types; prove that a COEA factors uniquely as a (...)
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  5.  9
    Graded Tensor Products of Quantum Logics.Robin Hudson & Sylvia Pulmannová - 1994 - Foundations of Physics 24 (1):109-116.
    Two notions of grading of a quantum logic by a product of copies of the group ℤ 2 are introduced and used to define graded tensor products of quantum logics.
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  6.  6
    Sum Logics and Tensor Products.Robin L. Hudson & Sylvia Pulmannová - 1993 - Foundations of Physics 23 (7):999-1024.
    A notion of factorizability for vector-valued measures on a quantum logic L enables us to pass from abstract logics to Hilbert space logics and thereby to construct tensor products. A claim by Kruszynski that, in effect, every orthogonally scattered measure is factorizable is shown to be false. Some criteria for factorizability are found.
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  7.  23
    Type-Decomposition of a Synaptic Algebra.David J. Foulis & Sylvia Pulmannová - 2013 - Foundations of Physics 43 (8):948-968.
    A synaptic algebra is a generalization of the self-adjoint part of a von Neumann algebra. In this article we extend to synaptic algebras the type-I/II/III decomposition of von Neumann algebras, AW∗-algebras, and JW-algebras.
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  8.  17
    Quantum Logics and Hilbert Space.Sylvia Pulmannová - 1994 - Foundations of Physics 24 (10):1403-1414.
    Starting with a quantum logic (a σ-orthomodular poset) L. a set of probabilistically motivated axioms is suggested to identify L with a standard quantum logic L(H) of all closed linear subspaces of a complex, separable, infinite-dimensional Hilbert space.
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  9.  12
    Quantum Logics and Quantum Measurements.Sylvia Pulmannová - 1999 - In Maria Luisa Dalla Chiara (ed.), Language, Quantum, Music. pp. 263--268.
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  10.  11
    Spin Factors as Generalized Hermitian Algebras.David J. Foulis & Sylvia Pulmannová - 2009 - Foundations of Physics 39 (3):237-255.
    We relate so-called spin factors and generalized Hermitian (GH-) algebras, both of which are partially ordered special Jordan algebras. Our main theorem states that positive-definite spin factors of dimension greater than one are mathematically equivalent to generalized Hermitian algebras of rank two.
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  11.  9
    Finitely Additive States and Completeness of Inner Product Spaces.Anatolij Dvurečenskij, Tibor Neubrunn & Sylvia Pulmannová - 1990 - Foundations of Physics 20 (9):1091-1102.
    For any unit vector in an inner product space S, we define a mapping on the system of all ⊥-closed subspaces of S, F(S), whose restriction on the system of all splitting subspaces of S, E(S), is always a finitely additive state. We show that S is complete iff at least one such mapping is a finitely additive state on F(S). Moreover, we give a completeness criterion via the existence of a regular finitely additive state on appropriate systems of subspaces. (...)
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  12.  8
    Relative Compatibility and Joint Distributions of Observables.Sylvia Pulmannová - 1980 - Foundations of Physics 10 (7-8):641-653.
    The notion of relative compatibility of observables is treated and its relation to the existence of joint distributions is obtained. The case of conventional quantum mechanics is studied and a generalization to the case of the quantum logic approach to quantum mechanics is given. It is shown that relative compatibility is equivalent to the existence of so-called “type 1” joint distributions.
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