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Mat. Zametki, 1977, Volume 22, Issue 3, Pages 345–356 (Mi mz8055)  

This article is cited in 1 scientific paper (total in 1 paper)

Weak continuity of metric projections

V. S. Balaganskii

Institute of Mathematics and Mechanics, Ural Scientific Center of the AS of USSR

Abstract: A necessary and sufficient condition is found for weak continuity of a metric projection onto a finite-dimensional subspace in $l_p$ ($1<p\ne2$). A metric projection onto a boundedly compact set in $l_p$ is sequentially weakly upper semicontinueus. An example is given on a convex, compact set in $l_2$ onto which the metric projection is not weakly continuous.

Full text: PDF file (886 kB)

English version:
Mathematical Notes, 1977, 22:3, 681–687

Bibliographic databases:

UDC: 517.5
Received: 29.06.1976

Citation: V. S. Balaganskii, “Weak continuity of metric projections”, Mat. Zametki, 22:3 (1977), 345–356; Math. Notes, 22:3 (1977), 681–687

Citation in format AMSBIB
\Bibitem{Bal77}
\by V.~S.~Balaganskii
\paper Weak continuity of metric projections
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 3
\pages 345--356
\mathnet{http://mi.mathnet.ru/mz8055}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=461103}
\zmath{https://zbmath.org/?q=an:0358.46009}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 3
\pages 681--687
\crossref{https://doi.org/10.1007/BF02412495}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. S. Balaganskii, L. P. Vlasov, “The problem of convexity of Chebyshev sets”, Russian Math. Surveys, 51:6 (1996), 1127–1190  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  • Математические заметки Mathematical Notes
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