no. 4
A spectral theory for order unit spaces
Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 35 (1981) no. 4, pp. 259-285. 
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     author = {Abbati, M. C. and Mani\`a, A.},
     title = {A spectral theory for order unit spaces},
     journal = {Annales de l'institut Henri Poincar\'e. Section A, Physique Th\'eorique},
     pages = {259--285},
     publisher = {Gauthier-Villars},
     volume = {35},
     number = {4},
     year = {1981},
     mrnumber = {650133},
     zbl = {0482.46006},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1981__35_4_259_0/}
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Abbati, M. C.; Manià, A. A spectral theory for order unit spaces. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 35 (1981) no. 4, pp. 259-285. http://www.numdam.org/item/AIHPA_1981__35_4_259_0/

[1] M.C. Abbati, A. Manià, Quantum Logic and Operational Quantum Mechanics. IFUM 227/FT to be published in Rep. Math. Phys. | MR | Zbl

[2] M.C. Abbati, A. Manià, The Quantum Logical and the Operational Description for Physical Systems. In Corrent Issues in Quantum Logic. Eds. E. Beltrametti and Bas C. Van Fraassen. E. Majorana, Int. Science Series Phys. Sciences, t. 8, Plenum Press, 1981. | MR

[3] E.M. Alfsen, Compact Convex Sets and Boundary Integrals. Ergebnisse der Mathematik und ihrer Grenzgebiete, t. 57, Springer, 1971. | MR | Zbl

[4] E.M. Alfsen, F.W. Shultz, Non Commutative Spectral Theory for Affine Function Spaces on Convex sets. Mem. Amer. Math. Soc., t. 172, 1976. | MR | Zbl

[5] E.M. Alfsen, F.W. Shultz, State Spaces of Jordan Algebras. Acta Math., t. 140, 1978, p. 155-190. | MR | Zbl

[6] E.M. Alfsen, H. Hanche-Olsen, F.W. Shultz, State Spaces of C*-algebras. Acta Math., t. 144, 1980, p. 267-305. | MR | Zbl

[7] E.M. Alfsen, F.W. Shultz and E. Størmer, A. Gelfand-Naimark Theorem for Jordan Algebras. Adv. in Math., t. 28, 1978, p. 11-56. | MR | Zbl

[8] P. Bonnet, Une Théorie Spectrale dans Certains Espaces de Banach Ordonnés. Prép. Université de Saint-Étienne. Départment de Mathématique, 1975.

[9] P. Bonnet, Une Théorie Spectrale dans Certains Espaces du type A(K). C. R. Acad. Sci., Paris, t. 282, 1976, Série A, p. 207-210. | MR | Zbl

[10] E.B. Davies, J.T. Lewis, An Operational Approach to Quantum Probability. Commun. Math. Phys., t. 16, 1970, p. 277-304. | MR | Zbl

[11] C.M. Edwards, The Operational Approach to Algebraic Quantum Theory I. Commun. Math. Phys., t. 16, 1970, p. 207-230. | MR | Zbl

[12] C.M. Edwards, Sets of Simple Observables in the Operational Approach to Quantum Theory. Ann. Inst. H. Poincaré, t. XV, n° 1, Sec. A, 1971, p. 1-14. | Numdam | MR | Zbl

[13] C.M. Edwards, Alternative Axioms for Statistical Physical Theories. Ann. Inst. H. Poincaré, t. XXII, n° 1, Sec. A, 1975, p. 81-95. | Numdam | MR | Zbl

[14] S.P. Gudder, Axiomatic Quantum Mechanics and Generalized Probability. In Probabilistic Methods in Applied Mathematics, A. Bharucha-Reid, Academic, New York, t. II, 1970. | Zbl

[15] P. Jordan, J. Von Neumann and E. Wigner, On an Algebraic Generalization of the Quantum Mechanical Formalism. Ann. of Math., 35, 1934, p. 29-64. | JFM | MR | Zbl

[16] R. Haag, D. Kastler, An Algebraic Approach to Quantum Field Theory. J. Math. Phys., t. 5, 1964, p. 846-861. | MR | Zbl

[17] P.R. Halmos, Measure Theory. Van Nostrand, 1950. | MR | Zbl

[18] P. Kruszynski, Some Problems in non Commutative Probability, Preprint. Proceedings of Colloquium on Random Fields : Rigorous Results in Statistical Mechanics and Q. F. T., Esztergom, 1979.

[19] G. Jameson, Ordered Linear Spaces, Springer, 1970. | MR | Zbl

[20] A.A. Lodkin, Every Measure on the Projections of a W*-algebra can be Extended to a State. Functional Analysis and its Applications, t. 8, 1974, p. 318 ; t. 9, 1975, p. 271, Erratum. | MR | Zbl

[21] G. Ludwig, Deutung des Begriffs « physicalische Theorie » und axiomatische Grundlegung der Hilbertaumstructure der Quantenmechanik durch Hauptsaetze des Messens, Lecture Notes in Physics, t. 4, Springer, 1970. | Zbl

[22] W. Luxemburg, A.C. Zaanen, Riesz Spaces I, North Holland, 1971. | MR | Zbl

[23] B. Mielnik, Theory of Filters, Commun. Math. Phys., t. 15, 1969, p. 1-46. | MR | Zbl

[24] B. Mielnik, Generalized Quantum Mechanics, Commun. Math. Phys., t. 37, 1974, p. 221-256. | MR

[25] B. Mielnik, Quantum Logics: is it Necessarily Orthocomplemented? In Quantum Mechanics, Determinism, Causality and Particles, p. 117-135. M. Flato et al (eds) D. Reidel Dordrech Holland, 1976.

[26] G.T. Rüttimann, Detectable Properties and Spectral Quantum Logics Marburg Conference on Interpretations and Foundations of Quantum Theories, 1979. | Zbl

[27] I.E. Segal, Postulates for General Quantum Mechanics. Annuals of Math., t. 48, 1947, p. 930-948. | MR | Zbl

[28] F.W. Shultz, On normed Jordan Algebras which are Banach Dual Spaces. J. Funct. Anal., t. 31, 1979, p. 360-376. | MR | Zbl

[29] V.S. Varadarajan, Probability in Physics and a Theorem on Simultaneous Observability. Com. Pure and Appl. Math., t. 15, 1962, p. 189-217. | MR | Zbl

[30] V.S. Varadarajan, Geometry of Quantum Theory, t. I. Van Nostrand Reinhold Comp., New York, 1970. | MR | Zbl

[31] G. Wittstock, Matrix order and W*-algebras in the operational approach to statistical systems. Commun. Math. Phys., t. 74, 1980, p. 61-70. | MR | Zbl