Korovkin's Theorem for Positive Functionals on Normed Algebras

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Authors

  • Balmohan Limaye
     Department of Mathematics, Indian Institute of Technology, Powai, Bombay - 400076 ,IN
  • Satish Shirali
     Department of Mathematics, Panjab University, Chandigarh - 160014 ,IN

Abstract

Korovkin's theorem [1] about convergence of positive operators on the space of all continuous functions on the unit interval or the unit circle has been generalized by several authors ([9], [6], [4], etc.).

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Published

1976-12-01

How to Cite

Limaye, B., & Shirali, S. (1976). Korovkin’s Theorem for Positive Functionals on Normed Algebras. The Journal of the Indian Mathematical Society, 40(1-4), 163–172. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/16622

Issue

Volume 40, Issue 1-4, March-December 1976

Section

Articles

License

Copyright (c) 1976 Balmohan Limaye, Satish Shirali

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

KOROVKIN, P.P., On the convergence of linear positive operators in the space of continuous functions, Dokl. Acad. Nauk SSSR, 90 (1953), 961-964 (Russian), M R 15, 236.

KOROVKIN, P.P., Linear Operators and Approximation Theory, Hindustan Publishing Corporation, Delhi (1960).

CHODA, H. and ECHIGO, M., On theorems of Korovkin, Proc. Japan Acad. 39 (1963), 107-108.

GROSSMAN, M.W., Note on a generalized Bohman-Korovkin theorem, J. Math. Anal. Appl., 45 (1974), 43-46.

LOOMIS, L.H., An Introduction to Abstract Harmonic Analysis, D. van Nostrand Company Inc., Princeton, N.J. (1953).

MOROZOV, E.N., Convergence of a sequence of positive linear operators in the space of continuous 2rc-periodic functions of two variables, Kalinin. Gos. Fed. Inst. Uc. Zap. 26(1958), 129-142 (Russian), MR 24A, 957.

NAIMARK, M.A., Normed Algebras, Wolters Noordhoff Publishing, Groningen, The Netherlands (1972).

RICKART,, C.E., General Theory of Banach Algebras, D. van Nostrand Company Inc., Princeton, N.J. (1960).

VOLKOV, V.I., On the convergence of sequences of linear positive operators in the space of continuous functions of two variables, Dokl. Akad. Nauk SSSR, 115, (1957), 17-19 (Russian), MR 20, 1205.