Banach-power-associative algebras and J-B algebras

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1. [1] A.A. Albert, On the power-associativity of rings, Summa Brasil, Math., t. 2, 1948, p. 21-32. Zbl0039.26403MR26044
2. [2] A.A. Albert, A theory of power-associative commutative algebras, Trans. Amer. Math. Soc., t. 69, 1950, p. 503-527. Zbl0039.26501MR38959
3. [3] E.M. Alfsen, Compact convex sets and boundary integrals, Ergebnisse der Math., t. 57, Springer-Verlag:Berlin, 1971. Zbl0209.42601MR445271
4. [4] E.M. Alfsen and F.W. Shultz, Non commutative spectral theory for affine function spaces on convex sets, Mem. Amer. Math. Soc., t. 172, 1976. Zbl0337.46013MR412822
5. [5] E.M. Alfsen and F.W. Shultz, On non commutative spectral theory and Jordan algebras, Proc. London Math. Soc., t. 38, 1979, p. 497-516. Zbl0404.46028MR532984
6. [6] E.M. Alfsen, F.W. Shultz and E. Størmer, A Guelfand-Neumark theorem for Jordan algebras, Adv. Math., t. 28, 1978, p. 11-56. Zbl0397.46065MR482210
7. [7] G.G. Emch, Algebraic methods in statistical mechanics and quantum field theory, Wiley-Interscience: New York, 1972. Zbl0235.46085
8. [8] W. Guz, Conditional probability in quantum axiomatic, Ann. Inst. H. Poincaré, 1980, p. 63-119. Zbl0454.03032MR593025
9. [9] R. Haag and D. Kastler, An algebraic approach to quantum field theory, J. Math. Phys., t. 5, 1964, p. 848-861. Zbl0139.46003MR165864
10. [10] H. Hanche-Olsen, A note on the bidual of a Jordan-Banach-algebra, Math. Z., t. 175, 1980, p. 29-31. Zbl0424.46036MR595629
11. [11] H. Hanche-Olsen and E. Størmer, Jordan operator algebras, Pitman, Boston, 1984. Zbl0561.46031MR755003
12. [12] B. Iochum, Cônes autopolaires et algèbres de Jordan, Lectures Notes in Math., 1049 Springer-Verlag, Berlin, 1984. Zbl0556.46040MR764767
13. [13] B. Iochum and F.W. Shultz, Normal state spaces of Jordan and von Neumann algebra, J. Functional Anal., t. 50, 1983, p. 317-328. Zbl0507.46055MR695418
14. [14] P. Jordan, J. Von Neumann and E. Wigner, On an algebraic generalization of the quantum mechanical formalism, Ann. of Math., t. 35, 1934, p. 29-64. Zbl0008.42103MR1503141JFM60.0902.02
15. [15] R.V. Kadison, A representation theory for commutative topological algebra, Mem. Amer. Math. Soc., t. 7, 1951. Zbl0042.34801MR44040
16. [16] R.V. Kadison, A generalized Schwarz inequality and algebraic invariants for operator algebras, Ann. Math., t. 56, 1952, p. 494-503. Zbl0047.35703MR51442
17. [17] L.A. Kokoris, Simple power associative algebras of degree two, Ann. of Math., t. 64, 1956, p. 544-550. Zbl0072.26202MR81273
18. [18] D.B. Lowdenslager, On postulates for general quantum mechanics, Proc. Amer. Math. Soc., t. 8, 1957, p. 88-91. Zbl0079.13003MR84741
19. [19] J. Von Neumann, On an algebraic generalization of the quantum mechanical formalism (Part I), Math. Sbornic, t. 1, 1936, p. 415-484. Zbl0015.24505
20. [20] S. Sakai, C* and W* algebras, Ergebnisse der Math., t. 60, Springer-Verlag, Berlin, 1971. Zbl0219.46042MR442701
21. [21] H.H. Schaeffer, Banach lattices and positive operators, Springer-Verlag, Berlin, 1974. Zbl0296.47023
22. [22] R.D. Schafer, An introduction to non associative algebras, Academic Press, New York, 1966. Zbl0145.25601MR210757
23. [23] S. Sherman, On Segal's postulates for general quantum mechanics, Ann. of Math., t. 64, 1956, p. 593-601. Zbl0075.21802MR82887
24. [24] F.W. Shultz, On normed Jordan algebras which are Banach dual spaces. J. Functional Anal., t. 31, 1979, p. 360-376. Zbl0421.46043MR531138
25. [25] I.E. Segal, Postulates for a general quantum mechanics, Ann. of Math., t. 48, 1947, p. 930-948. Zbl0034.06602MR22652
26. [26] R.R. Smith, On non-unital Jordan-Banach algebras, Math. Proc. Camb. Phil. Soc.. t. 82, 1977, p. 375-380. Zbl0372.46045MR467328

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