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Wittstock, Gerd

Matrix order and W*-algebras in the operational approach to statistical physical systems. (English) Zbl 0451.46046

Commun. Math. Phys. 74, 61-70 (1980).
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MSC:

46L60 Applications of selfadjoint operator algebras to physics
82B10 Quantum equilibrium statistical mechanics (general)
81P20 Stochastic mechanics (including stochastic electrodynamics)
46N99 Miscellaneous applications of functional analysis
46L10 General theory of von Neumann algebras

Keywords:

statistical physical system; operational approach; hereditary projections; complete matrix ordered base norm space; matrix order

Citations:

Zbl 0296.46059; Zbl 0341.46049
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Full Text: DOI

References:

[1] Alfsen, E.M., Shultz, F.W.: Non-commutative spectral theory for affine function spaces on convex sets. Memoir Am. Math. Soc.172 (1976) · Zbl 0337.46013
[2] Choi, Effros, E.G.: Injectivity and operator spaces. J. Funct. Anal.24, 156-209 (1977) · Zbl 0341.46049 · doi:10.1016/0022-1236(77)90052-0
[3] Choi, M.D.: Completely positive maps on complex matrices. Linear Algebra Appl.10, 285-290 (1975) · Zbl 0327.15018 · doi:10.1016/0024-3795(75)90075-0
[4] Connes, A.: Charactérisation des espaces vectoriels ordonnés sous-jacent aux algèbres de von Neumann. Ann. Inst. Fourier Grenoble24, 121-155 (1974) · Zbl 0287.46078
[5] Davies, E.B., Lewis, J.T.: An operational approach to quantum probability. Commun. Math. Phys.17, 239-260 (1970) · Zbl 0194.58304 · doi:10.1007/BF01647093
[6] Edwards, C.M.: Classes of operations in quantum theory. Commun. Math. Phys.20, 26-56 (1971) · Zbl 0203.57001 · doi:10.1007/BF01646732
[7] Effros, E.G.: Aspects of non-commutative order. In:C*-algebras and applications to physics. Lecture notes in mathematics650, 1-40 (1978) · doi:10.1007/BFb0067387
[8] Kraus, K.: Operations and effects in the Hilbert space formulation of quantum theory. In: Foundations of quantum mechanics and ordered linear spaces. Lecture notes in physics29, 206-229 (1974) · doi:10.1007/3-540-06725-6_17
[9] Lindblatt, G.: On the generator of quantum dynamical semigroups. Commun. Math. Phys.48, 119-130 (1975) · Zbl 0343.47031 · doi:10.1007/BF01608499
[10] Powers, R.T.: Selfadjoint algebras of unbounded operators. II. Transact. Am. Math. Soc.187, 261-293 (1974) · Zbl 0296.46059
[11] Schmitt, L.: Charakterisierung vonW*-Algebren durch autopolare 2-geordnete, diagonalhomogene, 2-positive Kegelpaare. Diplomarbeit, Universität des Saarlandes (1979)
[12] Werner, K.H.: Charakterisierung vonC*-Algebren durchp-Projektionen auf matrix-n-geordneten Räumen. Dissertation, Universität des Saarlandes (1979)
[13] Werner, K.H.: A characterisation ofC*-algebras by nh-projections on matrix ordered spaces. (To appear)
[14] Wils, W.: The ideal center of partially ordered vector spaces. Acta Math.127, 41-79 (1971) · Zbl 0224.46010 · doi:10.1007/BF02392051
[15] Wittstock, G.: Ordered normed tensor products. In: Foundations of quantum mechanics and ordered linear spaces. Lecture notes in physics29, 67-84 (1974) · doi:10.1007/3-540-06725-6_10
[16] Wittstock, G.: Ein operatorwertiger Hahn-Banach Satz. (To appear in J. Funct. Anal.)
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