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

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

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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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
2. Chobanyan S., Georgobiani G., “A Problem on Rearrangements of Summands in Normed Spaces and Rademacher Sums”, Lect. Notes Math., 1391 (1989), 33–46
3. Revesz S., “Rearrangement of Fourier-Series and Fourier-Series Whose Terms Have Random Signs”, Acta Math. Hung., 63:4 (1994), 395–402
4. Chasco M., Chobanyan S., “On Rearrangements of Series in Locally Convex Spaces”, Mich. Math. J., 44:3 (1997), 607–617
5. S. V. Konyagin, “On Uniformly Convergent Rearrangements of Trigonometric Fourier Series”, Journal of Mathematical Sciences, 155:1 (2008), 81–88
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
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