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Matematicheskie Zametki, 1972, Volume 11, Issue 2, Pages 209–214 (Mi mzm9781)  
This article is cited in 4 scientific papers (total in 4 papers)

Conditionally convergent series in a uniformly smooth Banach space

V. P. Fonf

Khar'kov Branch of the All-Union Design and Scientific-Research Institute of Industrial Transport
Full-text PDF (627 kB) Citations (4)
Abstract: The theorem of Steinitz on the form of the set of points which are sums of convergent rearrangements of a given series is extended to series ∑xk in the uniformly smooth Banach space X with modulus of smoothness ρ(t), satisfying the condition ∑ρ(||xk||)<∞.
Received: 12.10.1970
English version:
Mathematical Notes, 1972, Volume 11, Issue 2, Pages 129–132
DOI: https://doi.org/10.1007/BF01097931
Bibliographic databases:
Document Type: Article
UDC: 513.88
Language: Russian
Citation: V. P. Fonf, “Conditionally convergent series in a uniformly smooth Banach space”, Mat. Zametki, 11:2 (1972), 209–214; Math. Notes, 11:2 (1972), 129–132
Citation in format AMSBIB
\Bibitem{Fon72}
\by V.~P.~Fonf
\paper Conditionally convergent series in a uniformly smooth Banach space
\jour Mat. Zametki
\yr 1972
\vol 11
\issue 2
\pages 209--214
\mathnet{http://mi.mathnet.ru/mzm9781}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=298394}
\zmath{https://zbmath.org/?q=an:0252.46029}
\transl
\jour Math. Notes
\yr 1972
\vol 11
\issue 2
\pages 129--132
\crossref{https://doi.org/10.1007/BF01097931}
Linking options:
  • https://www.mathnet.ru/eng/mzm9781
  • https://www.mathnet.ru/eng/mzm/v11/i2/p209
    • This publication is cited in the following 4 articles:
    1. P. A. Borodin, K. S. Shklyaev, “Density of quantized approximations”, Russian Math. Surveys, 78:5 (2023), 797–851  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. P. A. Borodin, “Density of a semigroup in a Banach space”, Izv. Math., 78:6 (2014), 1079–1104  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. 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
    4. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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