Banach-power-associative algebras and J-B algebras

Iochum, Bruno ; Loupias, Guy

Annales de l'I.H.P. Physique théorique, Tome 43 (1985), p. 211-225 / Harvested from Numdam

Détail

Publié le : 1985-01-01

MR 817536 | Zbl 0587.17012 | 4 citations dans Numdam

Bibliographie

[1] A.A. Albert, On the power-associativity of rings, Summa Brasil, Math., t. 2, 1948, p. 21-32. | MR 26044 | Zbl 0039.26403

[2] A.A. Albert, A theory of power-associative commutative algebras, Trans. Amer. Math. Soc., t. 69, 1950, p. 503-527. | MR 38959 | Zbl 0039.26501

[3] E.M. Alfsen, Compact convex sets and boundary integrals, Ergebnisse der Math., t. 57, Springer-Verlag: Berlin, 1971. | MR 445271 | Zbl 0209.42601

[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. | MR 412822 | Zbl 0337.46013

[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. | MR 532984 | Zbl 0404.46028

[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. | MR 482210 | Zbl 0397.46065

[7] G.G. Emch, Algebraic methods in statistical mechanics and quantum field theory, Wiley-Interscience: New York, 1972. | Zbl 0235.46085

[8] W. Guz, Conditional probability in quantum axiomatic, Ann. Inst. H. Poincaré, 1980, p. 63-119. | Numdam | MR 593025 | Zbl 0454.03032

[9] R. Haag and D. Kastler, An algebraic approach to quantum field theory, J. Math. Phys., t. 5, 1964, p. 848-861. | MR 165864 | Zbl 0139.46003

[10] H. Hanche-Olsen, A note on the bidual of a Jordan-Banach-algebra, Math. Z., t. 175, 1980, p. 29-31. | MR 595629 | Zbl 0424.46036

[11] H. Hanche-Olsen and E. Størmer, Jordan operator algebras, Pitman, Boston, 1984. | MR 755003 | Zbl 0561.46031

[12] B. Iochum, Cônes autopolaires et algèbres de Jordan, Lectures Notes in Math., 1049 Springer-Verlag, Berlin, 1984. | MR 764767 | Zbl 0556.46040

[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. | MR 695418 | Zbl 0507.46055

[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. | JFM 60.0902.02 | MR 1503141 | Zbl 0008.42103

[15] R.V. Kadison, A representation theory for commutative topological algebra, Mem. Amer. Math. Soc., t. 7, 1951. | MR 44040 | Zbl 0042.34801

[16] R.V. Kadison, A generalized Schwarz inequality and algebraic invariants for operator algebras, Ann. Math., t. 56, 1952, p. 494-503. | MR 51442 | Zbl 0047.35703

[17] L.A. Kokoris, Simple power associative algebras of degree two, Ann. of Math., t. 64, 1956, p. 544-550. | MR 81273 | Zbl 0072.26202

[18] D.B. Lowdenslager, On postulates for general quantum mechanics, Proc. Amer. Math. Soc., t. 8, 1957, p. 88-91. | MR 84741 | Zbl 0079.13003

[19] J. Von Neumann, On an algebraic generalization of the quantum mechanical formalism (Part I), Math. Sbornic, t. 1, 1936, p. 415-484. | Zbl 0015.24505

[20] S. Sakai, C* and W* algebras, Ergebnisse der Math., t. 60, Springer-Verlag, Berlin, 1971. | MR 442701 | Zbl 0219.46042

[21] H.H. Schaeffer, Banach lattices and positive operators, Springer-Verlag, Berlin, 1974. | Zbl 0296.47023

[22] R.D. Schafer, An introduction to non associative algebras, Academic Press, New York, 1966. | MR 210757 | Zbl 0145.25601

[23] S. Sherman, On Segal's postulates for general quantum mechanics, Ann. of Math., t. 64, 1956, p. 593-601. | MR 82887 | Zbl 0075.21802

[24] F.W. Shultz, On normed Jordan algebras which are Banach dual spaces. J. Functional Anal., t. 31, 1979, p. 360-376. | MR 531138 | Zbl 0421.46043

[25] I.E. Segal, Postulates for a general quantum mechanics, Ann. of Math., t. 48, 1947, p. 930-948. | MR 22652 | Zbl 0034.06602

[26] R.R. Smith, On non-unital Jordan-Banach algebras, Math. Proc. Camb. Phil. Soc.. t. 82, 1977, p. 375-380. | MR 467328 | Zbl 0372.46045