Compression bases in effect algebras

• Autorzy: Gudder S.
• Języki publikacji: EN

Abstrakty

EN

We generalize David Foulis's concept of a compression base on a unital group to effect algebras. We first show that the compressions of a compressible effect algebra form a compression basis and that a sequential effect algebra possesses a natural maximal compression basis. It is then shown that many of the results concerning compressible effect algebras hold for arbitrary effect algebras by focusing on a specific compression base. For example, the foci (or projections) of a compression base form an orthomodular poset. Moreover, one can give a natural definition for the commutant of a projection in a compression base and results concerning order and compatibility of projections can be generalized. Finally it is shown that if a compression base has the projection-cover property, then the projections of the base form an orthomodular lattice

Słowa kluczowe

EN

effect algebra; abelian group; spectral resolution

PL

algebra efektywna; grupy abelowe; rozkłady spektralne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 1
• Strony: 43--54
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Gudder S.

• Department of Mathematics University of Denver, Denver, Colorado 80208, USA,

Bibliografia

• [1] M. K. Bennett and D. J. Foulis, Interval and scale effect algebras, Adv. Appl. Math. 91 (1997), 200.
• [2] P. Busch, P. J. Lahti and P. Middlestaedt, The Quantum Theory of Measurements, Springer-Verlag, Berlin, 1991.
• [3] P. Busch, M. Grabowski and P. J. Lahti, Operational Quantum Physics, Springer-Verlag, Berlin, 1995.
• [4] A. Dvurečenskij and S. Pulmannová, New Trends in Quantum Structures, Kluwer, Dordrecht, 2000.
• [5] D. J. Foulis, Compressible groups, Math. Slovaca, 53 (2003), 433
• [6] D. J. Foulis, Compressions on partially ordered abelian groups, Proc. Amer. Math. Soc. 132 (2004), 3581.
• [7] D. J. Foulis, Compressible groups with general comparability, Math. Slovaca (to appear).
• [8] D. J. Foulis, Spectral resolution in a Richart comgroup, Rep. Math. Phys. 54 (2004), 319.
• [9] D. J. Foulis, Compression bases in unital groups, Int. J. Theor. Phys. (to appear).
• [10] D. J. Foulis and M. K. Bennett, Effect algebras and unsharp quantum logics, Found. Phys. 24 (1994), 1325.
• [11] R. Giuntini and H. Greuling, Toward a formal language for unsharp properties, Found. Phys. 19 (1989), 931.
• [12] S. Gudder, Sharply dominating effect algebras, Tatra Mt. Math. Publ. 15 (1998), 23.
• [13] S. Gudder, Compressible effect algebras, Rep. Math. Phys. 54 (2004), 105.
• [14] S. Gudder and R. Greechie, Sequential products on effect algebras, Rep. Math. Phys. 49 (2002), 87.
• [15] S. Gudder and G. Nagy, Sequential quantum measurements, J. Math. Phys. 42 (2001), 5212.
• [16] K. Kraus, States, Effects and Operations, Springer-Verlag, Berlin, 1983.