RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 4, Pages 711–725 (Mi izv1528)  

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

On Fréchet spaces with certain classes of proximal subspaces

D. N. Zarnadze


Abstract: 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.
Bibliography: 23 titles.

Full text: PDF file (1920 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1987, 29:1, 67–79

Bibliographic databases:

UDC: 517.98
MSC: Primary 41A50, 46A06, 46A12, 46A25; Secondary 46B20
Received: 14.03.1983

Citation: 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
\Bibitem{Zar86}
\by D.~N.~Zarnadze
\paper On Fr\'echet spaces with certain classes of proximal subspaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 4
\pages 711--725
\mathnet{http://mi.mathnet.ru/izv1528}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=864172}
\zmath{https://zbmath.org/?q=an:0625.46005}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 29
\issue 1
\pages 67--79
\crossref{https://doi.org/10.1070/IM1987v029n01ABEH000959}


Linking options:
  • http://mi.mathnet.ru/eng/izv1528
  • http://mi.mathnet.ru/eng/izv/v50/i4/p711

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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 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
    2. 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  mathnet  crossref  mathscinet  zmath  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:202
    Full text:64
    References:37
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019