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Abstrakty
Aim of this short paper is to construct in any infinite-dimensional Hilbert space a series with terms tending to zero such that some of its rearrangements possess the discrete set of limit points.
Wydawca
Czasopismo
Rocznik
Tom
Strony
93--96
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
- Institute of Mathematics, Silesian University of Technology, Kaszubska 23, Gliwice 44-100, Poland
autor
- Institute of Mathematics, Silesian University of Technology, Kaszubska 23, Gliwice 44-100, Poland
autor
- Institute of Mathematics, Silesian University of Technology, Kaszubska 23, Gliwice 44-100, Poland
Bibliografia
- [1] S. Chobanyan, G. Giorgobiani, V. Kvaratskhelia and V. Tarieladze, A note on the rearrangement theorem in a Banach space, in: Information and Computer Technologies: Theory and Practice, Nova Publishers, Hauppauge (2012), 531-535.
- [2] J. Diestel, Sequences and Series in Banach Spaces, Springer-Verlag, New York, 1984.
- [3] V. Drobot, Rearrangements of series of functions, Trans. Amer. Math. Sac. 142 (1969), 239-248.
- [4] E. Freitag and R. Busam, Complex Analysis, Springer-Verlag, Berlin, 2005.
- [5] M. I. Kadets and V. M. Kadets, Series in Banach Space, Conditional and Unconditional Convergence, Birkhauser-Verlag, Basel, 1997.
- [6] M. I. Kadets and K. Woźniakowski, On series whose permutations have only two sum, Bull. Pol. Acad. Sci. Math. 37 (1989), 15-21.
- [7] V. M. Kadets, On some S. Banach’s problem (problem no. 106 from „Scottish Book”) (in Russian), Funktsional. Anal. i Prilozhen. 20 (1986), no. 4, 74-75.
- [8] V. M. Kadets, Sum regions of weakly convergent series (in Russian), Funktsional. Anal. i Prilozhen. 23 (1989), no. 2, 60-62; translation in Funct. Anal. Appl. 23 (1989), no. 2, 133-135.
- [9] V. M. Kadets, Weak and strong ranges of sums of a series in a Banach space (in Russian), Mat. Zametki 48 (1990), no. 2, 34-44; translation in Math. Notes Acad. Sci. USSR 48 (1990), no. 2, 743-748.
- [10] V. M. Kadets and M.1. Kadets, Rearrangements of Series with Elements in a Banach Space (in Russian), Tartuskij Gosudarstvennyj Universitet, Tartu, 1988; translation published by American Mathematical Society, Providence, 1991.
- [11] P.A. Kornilov, On range of sum of conditionally convergent series with functions terms, Mat. Sb. 137 (1988), 114-127.
- [12] S. Levental, V. Mandrekar and S. A. Chobanyan, Towards Nikishin’s theorem on the almost sure convergence of rearrange- ments of functional series, Funct. Anal. Appl. 45 (2011), no. 1, 33-45.
- [13] 0. S. Osipov, The integral analog of a series with a two-point sum range (in Russian), Sibirsk. Mat. Zh. 50 (2009), 1348-1355.
- [14] J. O. Wojtaszczyk, A series whose sum range is an arbitrary finite set, Studio Math. 171 (2005), no. 3, 261-281.
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Bibliografia
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bwmeta1.element.baztech-149b5d07-3579-4a4b-b95f-84b5455f75de