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Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 1, Pages 216–223 (Mi izv1952)  

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

Coefficient sequences in Hilbert and Banach space expansions

N. I. Gurarii


Abstract: In this article we prove some theorems about the sequences of coefficients which occur for expansions relative to a basis in a Banach space, and for a certain type of basis in $L_2[-\pi,\pi]$ investigated by K. I. Babenko, namely $\{|t|^\alpha e^{int}\}_{-\infty}^\infty$, $0<\alpha<1/2$. As an application of our results, we prove that there exists no universal basis in a separable Hilbert space.

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:1, 226–232

Bibliographic databases:

UDC: 513.8
MSC: 46B15
Received: 27.02.1969

Citation: N. I. Gurarii, “Coefficient sequences in Hilbert and Banach space expansions”, Izv. Akad. Nauk SSSR Ser. Mat., 35:1 (1971), 216–223; Math. USSR-Izv., 5:1 (1971), 226–232

Citation in format AMSBIB
\Bibitem{Gur71}
\by N.~I.~Gurarii
\paper Coefficient sequences in Hilbert and Banach space expansions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1971
\vol 35
\issue 1
\pages 216--223
\mathnet{http://mi.mathnet.ru/izv1952}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=278046}
\zmath{https://zbmath.org/?q=an:0214.12703}
\transl
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 1
\pages 226--232
\crossref{https://doi.org/10.1070/IM1971v005n01ABEH001039}


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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. St. Petersburg Math. J., 25:3 (2014), 361–396  mathnet  crossref  mathscinet  zmath  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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