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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 4, Pages 149–160 (Mi izv651)  

Smoothing of Hilbert-valued uniformly continuous maps

I. G. Tsar'kov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We approximate (in the uniform norm) Hilbert-valued uniformly continuous maps defined on $l_p$, $p\geqslant2$, by maps with bounded first derivatives and maximal local smoothness, which coincides with the smoothness of the space. The result obtained is definitive as far as the smoothness of smoothing maps is concerned since there is a 1-Lipschitzian map from $l_p$, $p\geqslant2$, to $l_2$ that cannot be approximated in the uniform metric by a map whose first derivative is uniformly continuous.

DOI: https://doi.org/10.4213/im651

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English version:
Izvestiya: Mathematics, 2005, 69:4, 149–160

Bibliographic databases:

UDC: 517.17
MSC: 46E30, 41A30, 41A25, 41A65, 46G05, 46E35
Received: 18.11.2004

Citation: I. G. Tsar'kov, “Smoothing of Hilbert-valued uniformly continuous maps”, Izv. RAN. Ser. Mat., 69:4 (2005), 149–160; Izv. Math., 69:4 (2005), 149–160

Citation in format AMSBIB
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\by I.~G.~Tsar'kov
\paper Smoothing of~Hilbert-valued uniformly continuous maps
\jour Izv. RAN. Ser. Mat.
\yr 2005
\vol 69
\issue 4
\pages 149--160
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\crossref{https://doi.org/10.4213/im651}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2170706}
\zmath{https://zbmath.org/?q=an:1103.41019}
\elib{http://elibrary.ru/item.asp?id=9195227}
\transl
\jour Izv. Math.
\yr 2005
\vol 69
\issue 4
\pages 149--160
\crossref{https://doi.org/10.1070/IM2005v069n04ABEH000541}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33645503867}


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  • https://doi.org/10.4213/im651
  • http://mi.mathnet.ru/eng/izv/v69/i4/p149

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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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