Geodesic
An extension of the Krein–Šmulian and Lozanovskii theorems to the case of metrizable spaces with a cone
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 1, pp. 126-131 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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L. V. Veselova; O. E. Tikhonov. An extension of the Krein–Šmulian and Lozanovskii theorems to the case of metrizable spaces with a cone. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 1, pp. 126-131. http://geodesic.mathdoc.fr/item/UZKU_2010_152_1_a11/

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