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排序方式: 共有54条查询结果,搜索用时 93 毫秒
1.
Filters and supports in orthoalgebras 总被引:3,自引:0,他引:3
D. J. Foulis R. J. Greechie G. T. Rüttimann 《International Journal of Theoretical Physics》1992,31(5):789-807
An orthoalgebra, which is a natural generalization of an orthomodular lattice or poset, may be viewed as a logic or proposition system and, under a welldefined set of circumstances, its elements may be classified according to the Aristotelian modalities: necessary, impossible, possible, and contingent. The necessary propositions band together to form a local filter, that is, a set that intersects every Boolean subalgebra in a filter. In this paper, we give a coherent account of the basic theory of Orthoalgebras, define and study filters, local filters, and associated structures, and prove a version of the compactness theorem in classical algebraic logic. 相似文献
2.
Observables, Calibration, and Effect Algebras 总被引:2,自引:0,他引:2
We introduce and study the D-model, which reflects the simplest situation in which one wants to calibrate an observable. We discuss the question of representing the statistics of the D-model in the context of an effect algebra. 相似文献
3.
D. J. Foulis M. K. Bennett R. J. Greechie 《International Journal of Theoretical Physics》1996,35(6):1117-1140
A test group is a pair (G, T) whereG is a partially ordered Abelian group andT is a generative antichain in its positive cone. It is shown here that effect algebras and algebraic test groups are coextensive, and a method for calculating the algebraic closure of a test group is developed. Some computational algorithms for studying finite effect algebras are introduced, and the problem of finding quotients of effect algebras is discussed. 相似文献
4.
5.
An RC-group is a unital group G with a distinguished compressionbase with respect to which G satisfies the Rickart projectionand general comparison properties. We prove that a monotone-complete RC-group is a union of subgroups each of which isa lattice-ordered Dedekind -complete RC-group. 相似文献
6.
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 direct sum of types I, II, and III; and obtain a generalization for COEAs of Ramsay’s fourfold decomposition of a complete orthomodular lattice. 相似文献
7.
A synaptic algebra is an abstract version of the partially ordered Jordan algebra of all bounded Hermitian operators on a
Hilbert space. We review the basic features of a synaptic algebra and then focus on the interaction between a synaptic algebra
and its orthomodular lattice of projections. Each element in a synaptic algebra determines and is determined by a one-parameter
family of projections—its spectral resolution. We observe that a synaptic algebra is commutative if and only if its projection
lattice is boolean, and we prove that any commutative synaptic algebra is isomorphic to a subalgebra of the Banach algebra
of all continuous functions on the Stone space of its boolean algebra of projections. We study the so-called range-closed
elements of a synaptic algebra, prove that (von Neumann) regular elements are range-closed, relate certain range-closed elements
to modular pairs of projections, show that the projections in a synaptic algebra form an M-symmetric orthomodular lattice,
and give several sufficient conditions for modularity of the projection lattice. 相似文献
8.
A generalized pseudo effect algebra (GPEA) is a partially ordered partial algebraic structure with a smallest element 0, but not necessarily with a unit (i.e, a largest element). If a GPEA admits a so-called unitizing automorphism, then it can be embedded as an order ideal in its so-called unitization, which does have a unit. We study unitizations of GPEAs with respect to a unitizing automorphism, paying special attention to the behavior of congruences, ideals, and the Riesz decomposition property in this setting. 相似文献
9.
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.
S. Pulmannová was supported by Research and Development Support Agency under the contract No. APVV-0071-06, grant VEGA 2/0032/09
and Center of Excellence SAS, CEPI I/2/2005. 相似文献
10.
David J. Foulis Sylvia Pulmannová 《International Journal of Theoretical Physics》2009,48(5):1320-1333
We refer to the real Jordan Banach algebra of bounded Hermitian operators on a Hilbert space as a Hermitian algebra. In this
paper we define and launch a study of a class of generalized Hermitian (GH) algebras. Among the examples of GH-algebras are
ordered special Jordan algebras, JW-algebras, and AJW-algebras, but unlike these more restricted cases, a GH-algebra is not
necessarily a Banach space and its lattice of projections is not necessarily complete. In this paper we develop the basic
theory of GH-algebras, identify their unit intervals as effect algebras, and observe that their projection lattices are sigma-complete
orthomodular lattices. We show that GH-algebras are spectral order-unit spaces and that they admit a substantial spectral
theory.
The second author was supported by Research and Development Support Agency under the contract No. APVV-0071-06, grant VEGA
2/0032/09 and Center of Excellence SAS, CEPI I/2/2005. 相似文献