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Mathematics of the USSR-Sbornik, 1983, Volume 45, Issue 4, Pages 507–513
DOI: https://doi.org/10.1070/SM1983v045n04ABEH001022 (Mi sm2232) 		 
On the connection between the properties of completeness and unconditional convergence for orthogonal systems

A. A. Talalyan
English version PDF (449 kB) Russian version article
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DOI: https://doi.org/10.1070/SM1983v045n04ABEH001022
Abstract: It is proved that there exists an orthonormal system that is not a system of unconditional convergence and, moreover, is not complete in the $L_2$-metric on any set of positive measure.
Bibliography: 8 titles.
Received: 05.08.1981
Bibliographic databases:
UDC: 517.52
MSC: Primary 42C10, 42C20, 42C30; Secondary 46B15, 46E30
Language: English
Original paper language: Russian
Citation: A. A. Talalyan, “On the connection between the properties of completeness and unconditional convergence for orthogonal systems”, Math. USSR-Sb., 45:4 (1983), 507–513
Citation in format AMSBIB
\Bibitem{Tal82}
\by A.~A.~Talalyan
\paper On the connection between the properties of completeness and unconditional convergence for orthogonal systems
\jour Math. USSR-Sb.
\yr 1983
\vol 45
\issue 4
\pages 507--513
\mathnet{http://mi.mathnet.ru//eng/sm2232}
\crossref{https://doi.org/10.1070/SM1983v045n04ABEH001022}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=651142}
\zmath{https://zbmath.org/?q=an:0519.42023}
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