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Mat. Sb. (N.S.), 1985, Volume 128(170), Number 1(9), Pages 50–65 (Mi msb2017)  

This article is cited in 6 scientific papers (total in 6 papers)

Structure of the set of sums of a conditionally convergent series in a normed space

S. A. Chobanyan


Abstract: Conditions are investigated for the set of sums of a conditionally convergent series with terms in a normed space to be linear. Main result: if $\sum a_k$ is a conditionally convergent series such that $\sum a_kr_k(s)$ converges for almost all $s$, then the set of sums of the series $\sum a_k$ is linear ($(r_k)$ is the sequence of Rademacher functions).
Bibliography: 24 titles.

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English version:
Mathematics of the USSR-Sbornik, 1987, 56:1, 49–62

Bibliographic databases:

UDC: 517.55
MSC: Primary 40A05, 40A30, 46B20; Secondary 42C20
Received: 27.06.1984

Citation: S. A. Chobanyan, “Structure of the set of sums of a conditionally convergent series in a normed space”, Mat. Sb. (N.S.), 128(170):1(9) (1985), 50–65; Math. USSR-Sb., 56:1 (1987), 49–62

Citation in format AMSBIB
\Bibitem{Cho85}
\by S.~A.~Chobanyan
\paper Structure of the set of sums of a~conditionally convergent series in a~normed space
\jour Mat. Sb. (N.S.)
\yr 1985
\vol 128(170)
\issue 1(9)
\pages 50--65
\mathnet{http://mi.mathnet.ru/msb2017}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=805695}
\zmath{https://zbmath.org/?q=an:0604.46015|0592.46013}
\transl
\jour Math. USSR-Sb.
\yr 1987
\vol 56
\issue 1
\pages 49--62
\crossref{https://doi.org/10.1070/SM1987v056n01ABEH003023}


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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. D. V. Pecherskii, “Rearrangements of series in Banach spaces and arrangements of signs”, Math. USSR-Sb., 63:1 (1989), 23–33  mathnet  crossref  mathscinet  zmath
    2. Chobanyan S., Georgobiani G., “A Problem on Rearrangements of Summands in Normed Spaces and Rademacher Sums”, Lect. Notes Math., 1391 (1989), 33–46  crossref  mathscinet  zmath  isi
    3. Revesz S., “Rearrangement of Fourier-Series and Fourier-Series Whose Terms Have Random Signs”, Acta Math. Hung., 63:4 (1994), 395–402  crossref  mathscinet  zmath  isi
    4. Chasco M., Chobanyan S., “On Rearrangements of Series in Locally Convex Spaces”, Mich. Math. J., 44:3 (1997), 607–617  crossref  mathscinet  zmath  isi
    5. S. V. Konyagin, “On Uniformly Convergent Rearrangements of Trigonometric Fourier Series”, Journal of Mathematical Sciences, 155:1 (2008), 81–88  mathnet  crossref  mathscinet  zmath  elib
    6. Sh. Levental, V. S. Mandrekar, S. A. Chobanyan, “Towards Nikishin's Theorem on the Almost Sure Convergence of Rearrangements of Functional Series”, Funct. Anal. Appl., 45:1 (2011), 33–45  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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