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Convergent sequences of linear operators in semiordered spaces

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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.

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Literature cited

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

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Translated from Matematicheskie Zametki, Vol. 8, No. 4, pp. 475–486, October, 1970.

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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

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Keywords

  • Linear Operator
  • Identity Operator
  • Convergent Sequence
  • Regular Operator
  • Semiordered Space