一类效应代数的态表示定理

Abstract

Abstract:

In 1994, Foulis and Bennett introduced effect algebra to represent the unsharp quantum logic structure. In this
paper, using the direct construction method, the authors present a state representation theorem of a class of effect algebras. That is, if Ω is a compact Hausdorff topological space, E(Ω)= {f: f ∈C(Ω, 0 ≤ f ≤ 1, then φ is a state of the effect algebra (E(Ω), Ο, 0, 1) if there exists a unique regular Borel probability measure μ on Ω such that for each f (E(Ω), Ο, 0, 1), φ (f) = ∫ _Ωf dμ.

Key words: Effect algebras, States, Representation theorem

CLC Number:

46A03

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LUO Lai-Zhen, LI Rong-Lu. The State Representation Theorem of a Class of Effect Algebras[J].Acta mathematica scientia,Series A, 2009, 29(6): 1518-1522.

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References

[1] Foulis D J, Bennett M K. Effect algebras and unsharp quantum logics. Found Phys, 1994, 24: 1331--1352

[2] Kadison R V, Ringrose J R. Fundamentals of the Theory of Operator Algebra. Graduate Studies in Mathematics. New York: American Mathematical Society, 1983

[3] Foulis D J, Greechie R, Ruttimann G. Filters and supports in orthoalgebras. Int J Theor Phys, 1992, 31: 789--802

[4] Miklos R. Quantun Logics and Algebraic Approach. Norwell: Kluwer Academic Publishers, 1998

[5] Dvurecenskij A, Pulmannova S. New Trends in Quantum Structures. Dordrecht, Boston, London: Kluwer Academic Publishers, 2000

[6] Bratteli O, Robinson D W. Operator Algebras and Quantum Statistical Mechanics. New York, Heidelberg, Berlin: Springer-Verlag, 1979

[7] Goodearl K. Partially Ordered Abelian Groups with Interpolation. Providence, RI: American Mathematical Society, 1986

[8] Pulmannova S. Effect algebras with riesz decomposition property and AF C*-algebras. Foundations of Physics, 1999, 29: 1389--1401

[9] Rudin W. Real and Complex Analysis. Beijing: China Machine Press, 2003

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The State Representation Theorem of a Class of Effect Algebras

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