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, 2010, Volume 152, Book 1,Pages <nobr>126

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

L. V. Veselova^a, O. E. Tikhonov^b

^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