Acta Mathematica

State spaces of C*-algebras

Erik M. Alfsen, Harald Hanche-Olsen, and Frederic W. Shultz

Full-text: Open access

Article information

Source
Acta Math., Volume 144 (1980), 267-305.

Dates
Received: 20 October 1979
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485890059

Digital Object Identifier
doi:10.1007/BF02392126

Mathematical Reviews number (MathSciNet)
MR573454

Zentralblatt MATH identifier
0426.46042

Rights
1980 © Almqvist & Wiksell

Citation

Alfsen, Erik M.; Hanche-Olsen, Harald; Shultz, Frederic W. State spaces of C * -algebras. Acta Math. 144 (1980), 267--305. doi:10.1007/BF02392126. https://projecteuclid.org/euclid.acta/1485890059


Export citation

References

  • Alfsen, E. M., Compact convex sets and boundary integrals. Ergebnisse der Math. 57, Springer Verlag, Berlin, 1971.
  • Alfsen, E. M. & Andersen, T. B., Split faces of compact convex sets. Proc. London Math. Soc., 21 (1970), 415–441.
  • Alfsen, E. M. & Effros, E., Structure in Banach spaces I–II. Ann. of Math., 96 (1972), 98–173.
  • Alfsen, E. M. & Shultz, F. W., Non-commutative spectral theory for affine function spaces on convex sets. Mem. Amer. Math. Soc., 172 (1976).
  • —, On non-commutative spectral theory and Jordan algebras. Proc. London Math. Soc., 38 (1979), 497–516.
  • Alfsen, E. M. & Shultz, F. W., State spaces of Jordan algebras. Acta Math., 140 (1978), 155–190.
  • Alfsen, E. M., Shultz, F. W. & Størmer, E., A Gelfand-Neumark theorem for Jordan algebras. Advances in Math., 28 (1978), 11–56.
  • Bellissard, J., Iochum, B. & Lima, R., Cônes autopolaires et facialement homogènes. C. R. Acad. Sci. Paris, 282 (1976), 1363–1365.
  • Bellissard, J. & Iochum, B., Homogeneous self-dual cones versus Jordan algebras, the theory revisited. Ann. Inst. Fourier (Grenoble), 28 (1978).
  • Bellissard, J. & Iochum, B., Spectral theory for homogeneous self-dual cones. Centre Phys. Théor. CNRS, Marseille, 1978. (Preprint.)
  • Choi, M. D., Positive linear maps for C*-algebras. Canadian J. Math., 24 (1972), 520–529.
  • —, A Schwarz inequality for positive linear maps of C*-algebras. Illinois J. Math., 18 (1974), 565–574.
  • Cohn, P. M., On homomorphic images of special Jordan algebras. Canadian J. Math., 6 (1954), 253–264.
  • Connes, A., Charactérisation des espaces vectoriels ordonnés sous-jacents aux algèbres de von Neumann. Ann. Inst. Fourier (Grenoble), 24 (1974), 121–155.
  • Dixmier, J., Les algèbres d'opérateurs dans l'espace hilbertien. Gauthier-Villars. Paris 1957.
  • —, Les C*-algèbres et leurs représentations. Gauthier-Villars, Paris 1969.
  • Effros, E. G., Order Ideals in a C*-algebra and its dual. Duke Math. J., 30 (1963), 391–412.
  • Effros, E. G. & Størmer, E., Jordan algebras of self-adjoint operators. Trans. Amer. Math. Soc., 127 (1967), 313–316.
  • Jordan, P., von Neumann, J. & Wigner, E., On an algebraic generalization of the quantum mechanical formalism. Ann. of Math., 35 (1934) 29–64.
  • Husemoller, D., Fibre bundles. McGraw-Hill, New York 1966.
  • Jacobson, N., Structure and representations of Jordan algebras Amer. Math. Soc. Colloq. Publ. 39, Providence R.I., 1968.
  • Jacobson, N. & Rickart, C., Homomorphisms of Jordan rings. Trans. Amer. Math. Soc., 69 (1950), 479–502.
  • Kaplansky, I., The structure of certain operator algebras. Trans. Amer. Math. Soc., 70 (1951), 219–255.
  • Kadison, R. V., A representation theory for commutative topological algebra. Mem. Amer. Math. Soc., 7 (1951).
  • —, Isometries of operator algebras. Ann. of Math., 54 (1951), 325–338.
  • —, Irreducible operator algebras. Proc. Nat. Acad. Sci. U.S.A., 43 (1955), 175–181.
  • —, Unitary invariants for representations of operator algebras. Ann. of Math., 66 (1957), 304–379.
  • —, States and representations. Trans. Amer. Math. Soc., 103 (1962), 304–319.
  • —, Transformation of states in operator theory and dynamics. Topology, Suppl. 2 (1967), 177–198.
  • von Neumann, J., On an algebraic generalization of the quantum mechanical formalism. Mat. Sbornik, 1 (1936), 415–482.
  • Prosser, R. T., On the ideal structure of operator algebras. Mem. Amer. Math. Soc., 45 (1963).
  • Segal, I. E., Postulates for general quantum mechanics. Ann. of Math., 48 (1947), 930–948.
  • Sakai, S., C*-algebras and W*-algebras. Ergebnisse der Math. 60, Springer Verlag, Berlin 1971.
  • Shultz, F. W., On normed Jordan algebras which are Banach dual spaces. J. Functional Analysis, 31 (1979), 360–376.
  • Stinespring, W. F., Positive functions on C*-algebras. Proc. Amer. Math. Soc., 6 (1955), 211–216.
  • Størmer, E., On the Jordan structure of C*-algebras. Trans Amer. Math. Soc., 120 (1965), 438–447.
  • —, Jordan algebras of type I. Acta Math., 115 (1966), 165–184.
  • —, On anti-automorphisms of von Neumann algebras. Pacific J. Math., 21 (1967) 349–370.
  • —, Irreducible Jordan algebras of self-adjoint operators. Trans. Amer. Math. Soc., 130 (1968), 153–166.
  • —, On partially ordered vector spaces and their duals, with applications to simplexes and C*-algebras. Proc. London Math. Soc., 18 (1968), 245–265.
  • Topping, D., Jordan algebras of self-adjoint operators. Mem. Amer. Math. Soc., 53 (1965).
  • —, An isomorphism invariant for spin factors. J. Math. and Mech., 15 (1966), 1055–1064.
  • Woronowicz, S. L., Positive maps of low dimensional matrix algebras. Rev. Math. Phys., 10 (1976) 105–187.
  • Maitland Wright, J. D., Jordan C*-algebras. Michigan Math. J., 24 (1977), 291–302.