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Mathematics of the USSR-Sbornik, 1990, Volume 65, Issue 1, Pages 119–131
DOI: https://doi.org/10.1070/SM1990v065n01ABEH001307 (Mi sm1773) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the set of sums of a conditionally convergent series of functions

P. A. Kornilov
English version PDF (711 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM1990v065n01ABEH001307
Abstract: This article concerns questions connected with the structure of the set of sums of series in a Banach space, i.e., the set of all limit functions for convergent rearrangements of a given series.
It is proved that in any Banach space there exist series for which the set of sums consists of two points, series for which it forms a finite or infinite arithmetic progression, and series for which it is a finite-dimensional lattice.
Stronger results are obtained separately for the spaces $L_p(0, 1)$ with $1\leqslant p<\infty$ and for convergence in measure of series of functions.
Bibliography: 5 titles.
Received: 17.03.1988
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1988, Volume 137(179), Number 1(9), Pages 114–127
Bibliographic databases:
UDC: 517.521
MSC: Primary 40A30, 42C20; Secondary 46E30, 28A20, 46B99
Language: English
Original paper language: Russian
Citation: P. A. Kornilov, “On the set of sums of a conditionally convergent series of functions”, Mat. Sb. (N.S.), 137(179):1(9) (1988), 114–127; Math. USSR-Sb., 65:1 (1990), 119–131
Citation in format AMSBIB
\Bibitem{Kor88}
\by P.~A.~Kornilov
\paper On the set of sums of a conditionally convergent series of functions
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 137(179)
\issue 1(9)
\pages 114--127
\mathnet{http://mi.mathnet.ru/sm1773}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=965883}
\zmath{https://zbmath.org/?q=an:0702.40005}
\transl
\jour Math. USSR-Sb.
\yr 1990
\vol 65
\issue 1
\pages 119--131
\crossref{https://doi.org/10.1070/SM1990v065n01ABEH001307}
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  • https://doi.org/10.1070/SM1990v065n01ABEH001307
  • https://www.mathnet.ru/eng/sm/v179/i1/p114
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:321
    Russian version PDF:113
    English version PDF:9
    References:36
     
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