Siberian Mathematical Journal

, Volume 17, Issue 2, pp 334–340 | Cite as

Some properties of the space of abstract affine functions on a Choquet simplex

  • G. M. ustinov


Affine Function Choquet Simplex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    A. J. Lazar, “Affine functions on simplexes and extreme operators,” Israel J. Math.5, No. 1, 31–43 (1967).Google Scholar
  2. 2.
    C. Foias and I. Singer, “Some remarks on the representation of linear operators in spaces of vector-valued continuous functions,” Rev. Roumaine Math. Pures et Appl.,2, No. 3-4, 729–752 (1960).Google Scholar
  3. 3.
    R. Phelps, Lectures on Choquet's Theorem [Russian translation], Mir, Moscow (1968).Google Scholar
  4. 4.
    Yu. A. Shashkin, “Convex sets, extremal points, simplexes,” in: Mathematical Analysis, Vol. 11 (Scientific and Technological Results) [in Russian], VINITI, Moscow (1973), pp. 5–50.Google Scholar
  5. 5.
    I. Singer, “Linear functionals on the space of continuous mappings of a bicompact Hausdorff space into a Banach space,” Rev. Roumaine Math. Pures et Appl.,2, 301–315 (1957).Google Scholar
  6. 6.
    J. Lindenstrauss, “Weakly compact sets—their topological properties and the Banach spaces they generate,” Ann. Math. Studies,69, 235–273 (1972).Google Scholar
  7. 7.
    A. J. Lazar, “Spaces of affine continuous functions on simplexes,” Trans. Amer. Math. Soc.,134, No. 3, 503–525 (1968).Google Scholar
  8. 8.
    L. Asimow and H. Atkinson, “Dominated extensions of continuous affine functions with range an ordered Banach space,” Quart. J. Math.,23, No. 92, 383–391 (1972).Google Scholar
  9. 9.
    E. B. Davies and G. F. Vincent-Smith, “Tensor products and projective limits of Choquet simplexes,” Math. Scand.,22, No. 1, 145–164 (1968).Google Scholar
  10. 10.
    Ng Kung-Fu, “The duality of partially ordered Banach spaces,” Proc. London Math. Soc.,19, No. 2, 269–288 (1969).Google Scholar
  11. 11.
    R. V. Kadison, “Transformations of states in operator theory and dynamics,” Topology,3, Suppl. 2, 177–198 (1965).Google Scholar
  12. 12.
    N. Dunford and J. T. Schwartz, Linear Operators [Russian translation], Izd. Inostr. Lit., Moscow (1962).Google Scholar
  13. 13.
    J. Lindenstrauss, “On subspaces of Banach spaces without quasicomplements,” Israel J. Math.6, No. 1, 36–39 (1968).Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • G. M. ustinov

There are no affiliations available

Personalised recommendations