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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
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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.
Received: 21.09.2009
Bibliographic databases:
Document Type: Article
UDC: 517.982.1+517.983.27
Language: Russian
Citation: L. V. Veselova, O. E. Tikhonov, “An extension of the Krein–Šmulian and Lozanovskii theorems to the case of metrizable spaces with a cone”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 152, no. 1, Kazan University, Kazan, 2010, 126–131
Citation in format AMSBIB
\Bibitem{VesTik10}
\by L.~V.~Veselova, O.~E.~Tikhonov
\paper An extension of the Krein--\v Smulian and Lozanovskii theorems to the case of metrizable spaces with a~cone
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2010
\vol 152
\issue 1
\pages 126--131
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku814}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3145244}
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