Acta Mathematica

State spaces of Jordan algebras

Erik M. Alfsen and Frederic W. Shultz

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Acta Math., Volume 140 (1978), 155-190.

Received: 3 January 1977
First available in Project Euclid: 31 January 2017

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1978 © Almqvist & Wiksell


Alfsen, Erik M.; Shultz, Frederic W. State spaces of Jordan algebras. Acta Math. 140 (1978), 155--190. doi:10.1007/BF02392307.

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  • Alfsen, E. M., Compact convex sets and boundary integrals. Ergebnisse der Math., 57, Springer Verlag, Berlin 1971.
  • Alfsen, E. M. & Shultz, F. W., Non-commutative spectral theory for affine function spaces on convex sets. Mem. Amer. Math. Soc., 172, Providence R.I., 1976.
  • Alfsen, E. M. & Shultz, F. W., On non-commutative spectral theory and Jordan algebras. Proc. London Math. Soc. To appear.
  • Alfsen, E. M., Shultz, F. W. & Størmer, E., A Gelfand-Neumark theorem for Jordan algebras. Advances in Math. To appear.
  • Birkhoff, G., Lattice theory. Amer. Math. Soc. Colloq Publ., Vol. 25, 3rd. edition, Providence, R.I. 1967.
  • Braun, H. & Koecher, M., Jordan Algebren. Springer Verlag, Berlin 1966.
  • Gunson, J., On the algebraic structure of quantum mechanics. Comm. Math. Phys., 6 (1967), 262–285.
  • Jacobson, N., Structure and representations of Jordan algebras. Amer. Math. Soc. Colloq. Publ. Vol. 39, Providence R.I. 1968.
  • Jordan, P., von Neumann, J., & Wigner, E., On an algebraic generalization of the quantum mechanical formalism. Ann. of Math., 35 (1934), 29–64.
  • Maclaren, M. D., Atomic orthocomplemented lattices. Pacific J. Math., 14 (1964), 597–612.
  • Maeda, F. & Maeda, S., Theory of symmetric lattices. Grundlehren der math. Wissensch., No. 173, Springer Verlag, Berlin 1970.
  • Mielnik, B., Theory of filters. Comm. Math. Phys., 15 (1969), 1–46.
  • von Neumann, J., On an algebraic generalization of the quantum mechanical formalism, Part I. Mat. Sb., 1 (1936), 415–484.
  • Pool, J. C. T., Semimodularity and the logic of quantum mechanics. Comm. Math. Phys., 9 (1968), 218–228.
  • Schreiner, E., Modular pairs in orthomodular lattices. Pacific J. Math., 91 (1966), 519–528.
  • Segal, I. E., Postulates for general quantum mechanics. Ann. of Math., 48 (1947), 930–948.
  • Shultz, F. W., On normed Jordan algebras which are Banach dual spaces, J. Functional Analysis. To appear.
  • Topping, D., Jordan algebras of self-adjoint operators. Mem. Amer. Math. Soc., 53, Providence R.I., 1965.
  • —, An isomorphism invariant for spin factors. J. Math. Mech., 15 (1966), 1055–1064.
  • —, Asymptoticity and semimodularity in projection lattices. Pacific J. Math., 20 (1967), 317–325.