Axiomatique quantique et algèbres normées non associatives
Annales scientifiques de l'Université de Clermont. Mathématiques, Tome 97 (1991) no. 27, pp. 59-91. 
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     author = {Loupias, Guy},
     title = {Axiomatique quantique et alg\`ebres norm\'ees non associatives},
     journal = {Annales scientifiques de l'Universit\'e de Clermont. Math\'ematiques},
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     volume = {97},
     number = {27},
     year = {1991},
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     url = {http://archive.numdam.org/item/ASCFM_1991__97_27_59_0/}
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Loupias, Guy. Axiomatique quantique et algèbres normées non associatives. Annales scientifiques de l'Université de Clermont. Mathématiques, Tome 97 (1991) no. 27, pp. 59-91. http://archive.numdam.org/item/ASCFM_1991__97_27_59_0/

1 P. Jordan, J. Von Neumann and E. Wigner, On an algebraic generalization of the quantum machanical formalism. Ann. of Math. t.35, 1934, p. 29-64. | MR | Zbl

2 I.E. Segal, Postulates for a general quantum machanic. Ann. of Math. T. 48, 1947, p. 930-948. | MR | Zbl

3 R. Haag and D. Kastler, An algebraic approach to quantum field theory. J. Math. Phys. t.5, 1964, p. 848-861. | MR | Zbl

4 H. Hanche-Olsen and E. Stormer, Jordan operator algebras. Pitman, Boston, 1984. | MR | Zbl

5 E.M. Alfsen, Compact convex sets and boundary integrals. Ergebnisse der Math. t. 57, Springer-Verlag, Berlin, 1971. | MR | Zbl

6 G.C. Wick, A.S. Wightman and E.P. Wigner, Intrinsic parity of elementary particles, Phys. Rev. t. 88, 1952, p. 101-105. | MR | Zbl

7 C. Cohen-Tànnoudji, B. Diu et F. Laloe, Mécanique quantique. Hermann, Paris, 1973.

8 R. Haag, N.M. Hugenholtz and M. Winnink, On the equilibrium states in quantum statistical mechanics. Commun. Math. Phys. t. 5, 1967, p. 215-236. | MR | Zbl

9 J. Von Neumann, Die eindentigkeit der Schrôdingerschen operatoren. Math. Ann. t. 104, 1931, p. 570-578. | MR | Zbl

10 R. Haag, On quantum field theories. Mat.-Fys. Medd. Danske Vid. Selsk, t. 29, 1955, p. 1-37. | MR | Zbl

11 J.M.G. Fell, The dual space of C*-algebras. Trans. Amer. Math. Soc., t. 94, 1960, p. 365-403. | MR | Zbl

12 G. Birkhoff and J. Von Neumann, The logic of quantum mechanics. Ann. of Math., t. 37, 1936, p. 823-843. | MR | Zbl

13 G.G. Emch, Algebraic methods in statistical mechanics and quantum field theory. Wileyl-Interscience, New-York, 1972. | Zbl

14 B. Iochum and G. Loupias, Banach power associative algebras and JB-algebras. Ann. Inst. H. Poincaré, t. 43, 1985, p. 211-225. | Numdam | MR | Zbl

15 E.M. Alfsen, F.W. Shultz and E. Stomer, A Gelfand-Neumark theorem for Jordan algebras. Adv. Math., t. 28, 1978, p. 11-56. | MR | Zbl

16 E. Stomer, Jordan algebras versus C*-algebras. Acta Phys. Aust. t. XVI, 1976, p. 1-14. | MR

17 I. Segal, Mathematical problems in relativistic physics. Amer. Math. Society, Providence, 1963. | MR | Zbl

18 G.W. Mackey, Mathematical foundations of quantum mechanics. Benjamin, New-York, 1963. | Zbl

19 A.M. Gleason, Measures on the closed subspaces of a Hilbert space. J. Rat. Mech. Analysis, t. 6, 1957, p. 885-894. | MR | Zbl

20 W. Guz, Conditional probability in quantum axiomatic. Ann. Inst. H. Poincaré, t. 33, 1980, p. 63-119. | Numdam | MR | Zbl

21 E.M. Alfsen and F.W. Shultz, Non commutative spectral theory for affine functions spaces on convex sets. Mem. Amer. Math. Soc. t. 172, 1976. | MR | Zbl

22 E.M. Alfsen and F.W. Shultz, On non commutative spectral theory and Jordan algebras. Proc. London Math. Soc., t. 38, 1979, p. 497-526. | Zbl

23 M.A. Youngson, Hermitian operators on Banach Jordan algebras. Proc. Edinburgh Math. Soc., t. 22, 1979, p. 169-180. | MR | Zbl

24 H.N. Boyadjiev and M.S. Youngson, Alternators on Banach Jordan algebras. Comptes Rendus Académie Bulgare des Sciences, t. 33, 1980, p. 1589-1590. | MR | Zbl

25 L.J. Bunce, On compact action in JB-algebras. Proc. Edinburgh Math. Soc. t. 26, 1983, p 353-360. | MR | Zbl

26 B. Aupetit, Propriétés spectrales des algèbres de Banach. Lecture Notes in Math., t. 735, 1979. | MR | Zbl