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Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 4, Pages 821–830 (Mi izv1853)  

This article is cited in 2 scientific papers (total in 2 papers)

Reflexivity and best approximations in Fréchet spaces

D. N. Zarnadze


Abstract: The paper gives a negative answer to the following question of M. Wriedt: Is it true that in every projective limit of reflexive Banach spaces there exists a normlike metric for which all closed hyperplanes are proximinal?
In particular, it is shown that if $E[\mathfrak T]$ is a nuclear Fréchet space nonisomorphic to the space of all sequences $\omega$, then for an arbitrary normlike metric $d$ on $E$ inducing the topology $\mathfrak T$, there exist nonproximinal closed hyperplanes.
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1981, 17:1, 87–94

Bibliographic databases:

UDC: 513.88
MSC: 46A06, 46A25, 41A50, 41A65
Received: 11.03.1979

Citation: D. N. Zarnadze, “Reflexivity and best approximations in Fréchet spaces”, Izv. Akad. Nauk SSSR Ser. Mat., 44:4 (1980), 821–830; Math. USSR-Izv., 17:1 (1981), 87–94

Citation in format AMSBIB
\Bibitem{Zar80}
\by D.~N.~Zarnadze
\paper Reflexivity and best approximations in Fr\'echet spaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 4
\pages 821--830
\mathnet{http://mi.mathnet.ru/izv1853}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=587339}
\zmath{https://zbmath.org/?q=an:0463.46001|0454.46003}
\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 17
\issue 1
\pages 87--94
\crossref{https://doi.org/10.1070/IM1981v017n01ABEH001331}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MW12300004}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. N. Zarnadze, “On Fréchet spaces with certain classes of proximal subspaces”, Math. USSR-Izv., 29:1 (1987), 67–79  mathnet  crossref  mathscinet  zmath
    2. D. N. Zarnadze, “On some topological and geometrical properties of Frechet–Hilbert spaces”, Russian Acad. Sci. Izv. Math., 41:2 (1993), 273–288  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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