Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

A characterization of generalized and classical best approximation elements relative to spaces of finite codimension

  • 27 Accesses

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

Literature cited

  1. 1.

    A. L. Garkavi, “Duality theorems for approximations by elements in convex sets,” Usp. Mat. Nauk,16, No. 4, 141–145 (1961).

  2. 2.

    A. L. Garkavi, “The Helly problem and best approximation of summable functions,” Mat. Sb.,84, No. 2, 196–217 (1971).

  3. 3.

    L. P. Vlasov, “Generalized best approximation elements,” Mat. Zametki,19, No. 4, 513–523 (1976).

  4. 4.

    L. P. Vlasov, “Properties of generalized best approximation elements,” Mat. Zametki,24, No. 4, 513–522 (1978).

  5. 5.

    L. P. Vlasov, “Uniqueness of generalized best approximation elements,” Mat. Zametki,25, No. 2, 161–175 (1979).

  6. 6.

    V. D. Mil'man, “Geometric theory of Banach spaces, Part I. Theory of basis and minimal systems,” Usp. Mat. Nauk,25, No. 3, 113–174 (1970).

  7. 7.

    I. Singer, Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Springer-Verlag, New York (1970).

  8. 8.

    I. Singer, The Theory of Best Approximation and Functional Analysis, SIAM Regional Conf. Series in Appl. Math., Vol. 13, Philadelphia (1974).

  9. 9.

    L. P. Vlasov, “Approximating properties of subspaces of finite codimension in C(Q),” Mat. Zametki,28, No. 2, 205–222 (1980).

  10. 10.

    M. M. Day, Normed Linear Spaces, Springer-Verlag (1973).

Download references

Author information

Additional information

Translated from Matematicheskie Zametki, Vol. 28, No. 5, pp. 707–716, November, 1980.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Vlasov, L.P. A characterization of generalized and classical best approximation elements relative to spaces of finite codimension. Mathematical Notes of the Academy of Sciences of the USSR 28, 809–813 (1980). https://doi.org/10.1007/BF01141086

Download citation

Keywords

  • Approximation Element
  • Finite Codimension
  • Good Approximation Element
  • Classical Good Approximation