This article is cited in 2 scientific papers (total in 2 papers)
On Fréchet spaces with certain classes of proximal subspaces
D. N. Zarnadze
A new metric with absolutely convex balls is introduced on a metrizable locally convex space. Necessary and sufficient conditions are given for all closed hypersubspaces and all nonnormable closed subspaces of a Fréchet space to be proximal, i.e., to have the property that there exist elements of best approximation with respect to this metric. In particular, these conditions are expressed in terms of the topologies of the original space and the strong dual space. It is proved that the Fréchet spaces $B\times\omega$ have the proximality property, where $B$ is a reflexive Banach space and $\omega=R^N$ is the nuclear Fréchet space of all numerical sequences. Questions of Albinus and Wriedt are answered.
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Mathematics of the USSR-Izvestiya, 1987, 29:1, 67–79
MSC: Primary 41A50, 46A06, 46A12, 46A25; Secondary 46B20
D. N. Zarnadze, “On Fréchet spaces with certain classes of proximal subspaces”, Izv. Akad. Nauk SSSR Ser. Mat., 50:4 (1986), 711–725; Math. USSR-Izv., 29:1 (1987), 67–79
Citation in format AMSBIB
\paper On Fr\'echet spaces with certain classes of proximal subspaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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This publication is cited in the following articles:
D. N. Zarnadze, “On some topological and geometrical properties of Frechet–Hilbert spaces”, Russian Acad. Sci. Izv. Math., 41:2 (1993), 273–288
D. N. Zarnadze, “A generalization of the method of least squares for operator equations in some Frechet spaces”, Izv. Math., 59:5 (1995), 935–948
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