Abstract
The definition given by P. P. Korovkin of operators of the class Sm and conditions for the convergence of these operators to the identity operator are extended to apply to regular operators from a K-space R0 with a unit, into a K-space R1 where R0 and R1 are normally contained in the union of the spaces S [a, b] and s.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
P. P. Korovkin, “Convergent sequences of linear operators,” Uspekhi Matem. Nauk,17, No. 4, 147–152 (1962).
B. Z. Vulikh, Introduction to the Theory of Partially Ordered Spaces [in Russian], Moscow (1961).
V. A. Rokhlin, “Fundamental concepts in measure theory,” Matem. Sb.,25, No. 1, 107–150 (1949).
L. V. Kantorovich, B. Z. Vulikh, and A. G. Pinsker, Functional Analysis in Partially Ordered Spaces [in Russian], Moscow-Leningrad (1950).
P. P. Korovkin, “The order of approximations of functions by linear polynomial operators of the class Sm,” in: Investigations of Contemporary Problems in Constructive Function Theory [in Russian], Baku (1965), pp. 163–166.
T. Ogasawara, “Theory of vector lattices,” I, Sci. Hiroshima Univ., Ser. A,12, 37–100 (1942).
G. Ya. Lozanovskii, “Isomorphic Banach lattices,” Sibirsk. Matem. Zh.,10, No. 1, 93–98 (1969).
M. Krein and S. Krein, “Sur l'espace des fonctions continues définies sur un bicompact de Hausdorff et ses sousespaces semiordonnés,” Matem. Sb.,13, No. 1, 1–37 (1943).
M. A. Krasnosel'skii and E. A. Lifshits, “The convergence of sequences of positive operators in linear topological space,” Jspekhi Matem. Nauk,23, No. 2, 213–214 (1968).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 8, No. 4, pp. 475–486, October, 1970.
Rights and permissions
About this article
Cite this article
Vasil'ev, R.K. Convergent sequences of linear operators in semiordered spaces. Mathematical Notes of the Academy of Sciences of the USSR 8, 736–741 (1970). https://doi.org/10.1007/BF01104374
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01104374