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Mat. Zametki, 1973, Volume 14, Issue 1, Pages 31–38 (Mi mz7200)  

This article is cited in 3 scientific papers (total in 4 papers)

Rearrangements of series in $L_p$

E. M. Nikishin

M. V. Lomonosov Moscow State University

Abstract: In this note we show that the condition
$$\sqrt{\sum_{n=1}^\infty f_n^2(x)}\in L_p$$
is sufficient for the set of sums of the rearranged series $\Sigma_\sigma f_n$ to be a closed linear set in $L_p$.

Full text: PDF file (333 kB)

English version:
Mathematical Notes, 1973, 14:1, 570–574

Bibliographic databases:

UDC: 517.5
Received: 21.02.1973

Citation: E. M. Nikishin, “Rearrangements of series in $L_p$”, Mat. Zametki, 14:1 (1973), 31–38; Math. Notes, 14:1 (1973), 570–574

Citation in format AMSBIB
\Bibitem{Nik73}
\by E.~M.~Nikishin
\paper Rearrangements of series in $L_p$
\jour Mat. Zametki
\yr 1973
\vol 14
\issue 1
\pages 31--38
\mathnet{http://mi.mathnet.ru/mz7200}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=330835}
\zmath{https://zbmath.org/?q=an:0278.40003}
\transl
\jour Math. Notes
\yr 1973
\vol 14
\issue 1
\pages 570--574
\crossref{https://doi.org/10.1007/BF01095771}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. V. Pecherskii, “A theorem on projections of rearranged series with terms in $L_p$”, Math. USSR-Izv., 11:1 (1977), 193–204  mathnet  crossref  mathscinet  zmath
    2. S. A. Chobanyan, “Structure of the set of sums of a conditionally convergent series in a normed space”, Math. USSR-Sb., 56:1 (1987), 49–62  mathnet  crossref  mathscinet  zmath
    3. A. G. Vitushkin, A. A. Gonchar, B. S. Kashin, A. I. Kostrikin, S. M. Nikol'skii, S. P. Novikov, P. L. Ul'yanov, L. D. Faddeev, “Evgenii Mikhailovich Nikishin (obituary)”, Russian Math. Surveys, 42:5 (1987), 153–160  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. 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
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