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 ∑ak is a conditionally convergent series such that ∑akrk(s) converges for almost all s, then the set of sums of the series ∑ak is linear ((rk) is the sequence of Rademacher functions).
Bibliography: 24 titles.
\Bibitem{Cho85}
\by S.~A.~Chobanyan
\paper Structure of the set of sums of a~conditionally convergent series in a~normed space
\jour Math. USSR-Sb.
\yr 1987
\vol 56
\issue 1
\pages 49--62
\mathnet{http://mi.mathnet.ru/eng/sm2017}
\crossref{https://doi.org/10.1070/SM1987v056n01ABEH003023}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=805695}
\zmath{https://zbmath.org/?q=an:0604.46015|0592.46013}
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https://www.mathnet.ru/eng/sm2017
https://doi.org/10.1070/SM1987v056n01ABEH003023
https://www.mathnet.ru/eng/sm/v170/i1/p50
This publication is cited in the following 8 articles:
S. V. Konyagin, Y. V. Malykhin, “Basis sets in Banach spaces”, Springer Optimization and Its Applications, 68 (2012), 381–386
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
S. V. Konyagin, “On Uniformly Convergent Rearrangements of Trigonometric Fourier Series”, Journal of Mathematical Sciences, 155:1 (2008), 81–88
Chasco M., Chobanyan S., “On Rearrangements of Series in Locally Convex Spaces”, Mich. Math. J., 44:3 (1997), 607–617
P. G. Dodds, F. A. Sukochev, “RUC-decompositions in symmetric operator spaces”, Integr equ oper theory, 29:3 (1997), 269
Revesz S., “Rearrangement of Fourier-Series and Fourier-Series Whose Terms Have Random Signs”, Acta Math. Hung., 63:4 (1994), 395–402
Chobanyan S., Georgobiani G., “A Problem on Rearrangements of Summands in Normed Spaces and Rademacher Sums”, Lect. Notes Math., 1391 (1989), 33–46
D. V. Pecherskii, “Rearrangements of series in Banach spaces and arrangements of signs”, Math. USSR-Sb., 63:1 (1989), 23–33
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