Skip to main content
SpringerLink
Log in

On complemented subspaces of simplex spaces

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

Jellett's theorem about the resolution of the space, A(X) of continuous affine functions on a compact ahoquet simplex X into a direct sum is generalized to simplex spaces. A new characteristic property of the space A(X), dual tol 1(Γ), is given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. S. Eilenberg, “Banach space methods in topology,” Ann. of Math.,43, No. 3, 568–579 (1942).

    Google Scholar 

  2. F. Jellett, “On the direct sum decomposition of the affine space of a choquet simplex,” Quart. J. Math.,18, No. 71, 233–237 (1967).

    Google Scholar 

  3. E. M. Alfsen, Compact Convex Sets and Boundary Integrals, Springer-Verlag (1971).

  4. R. Phelps, Lectures on Choquet's Theorem, Van Nostrand (1966).

  5. E. G. Effros, “Structure in Simplexes,” Acta. Math.,117, 103–121 (1967).

    Google Scholar 

  6. N. Dunford and J. T. Schwartz, Linear Operators, Vol. I, Interscience (1958).

  7. M. Rcogalski, “Etude du quotient d'un Simplexe par une fae fermée et application a un théorème de Alfsen; Quotient par une relation d'équivalence,” Seminaire Brelot-Choquet (Theorie du Potentiel), No. 2, 2/01–2/25 (1967/68).

    Google Scholar 

  8. H. E. Lacey and P. D. Morris, “On spaces of type A(K) and their duals,” Proc. Amer. Math. Soc.,23, No. 1, 151–157 (1969).

    Google Scholar 

  9. V. D. Mil'man, “Geometric theory of Banach spaces, I,” Uspekhi Matem. Nauk,25, No. 3, 113–175 (1970).

    Google Scholar 

  10. V. I. Gurarii and N. I. Gurarii, “On a sequential property of the spacel 1,” Matem. Issledovaniya,4, No. 3, 140–145 (1969).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics and Mechanics Institute, Academy of Sciences of the USSR, USSR

    G. M. Ustinov

Authors
  1. G. M. Ustinov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 16, No. 5, pp. 751–761, November, 1974.

In conclusion, the author expresses his gratitude to Yu. A. Shashkin for useful discussions and help in the preparation of this article.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ustinov, G.M. On complemented subspaces of simplex spaces. Mathematical Notes of the Academy of Sciences of the USSR 16, 1044–1049 (1974). https://doi.org/10.1007/BF01149795

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01149795

Keywords

Search

Navigation