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JOURNALS // Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki // Archive

Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2010 Volume 152, Book 1, Pages 126–131 (Mi uzku814)

An extension of the Krein–Šmulian and Lozanovskii theorems to the case of metrizable spaces with a cone

L. V. Veselovaa, O. E. Tikhonovb

a Kazan State Technological University
b Kazan State University, The Faculty of Computer Science and Cybernetics

Abstract: The Krein–Šmulian theorem and a Lozanovskii result on automatical continuity of positive linear operators are extended to the case of complete metrizable topological vector spaces.

Keywords: metrizable topological vector spaces, cone, positive linear operator, Krein–Šmulian theorem.

UDC: 517.982.1+517.983.27

Received: 21.09.2009



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