Skip to main content
Log in

On the convergence of linear operators of the class Sm

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

Abstract

We give a necessary and sufficient condition for the convergence of sequences of operators of the class Sm to a single operator.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

Literature cited

  1. P. P. Korovkin, “Convergent sequences of linear operators,” Uspekhi Mat. Nauk,17, No. 4, 147–152 (1962).

    Google Scholar 

  2. L. M. Zybin, “On the conditions for the convergence of a sequence of linear operators of the class Sm,” Ucheb. Zap. Novgorodsk. Ped. Inst.,7, 36–43 (1966).

    Google Scholar 

  3. Yu. A. Shashkin, “Korovkin systems in spaces of continuous functions,” Izv. Akad. Nauk SSSR. Ser. Matem.,26, No. 4, 495–512 (1962).

    Google Scholar 

  4. C. Carathéodory, “Über den Variabilitätsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen,” Rend. Circ. Mat. Palermo,36, No. 2, 193–217 (1911).

    Google Scholar 

  5. L. Danzer, B. Grünbaum, and V. Klee, Helly's Theorem and Its Relatives, Proceedings of Symposia in Pure Mathematics, Vol. VII, Convexity, Amer. Math. Soc., Providence, R. I. (1963), pp. 101–180.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 6, No. 5, pp. 591–598, November, 1969.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Min'kova, R.M., Shashkin, Y.A. On the convergence of linear operators of the class Sm . Mathematical Notes of the Academy of Sciences of the USSR 6, 816–820 (1969). https://doi.org/10.1007/BF01101410

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01101410

Keywords

Navigation