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Mat. Zametki, 1976, Volume 19, Issue 5, Pages 707–716 (Mi mz7791)  

The kernel of a sequence obtained from a given sequence with the aid of a regular transformation

A. A. Shcherbakov

Ural State University

Abstract: The smallest set is found that contains the kernel of a sequence obtained from a sequence of elements $\{x_n\}$ of a Banach space with the aid of a regular transformation of the class $T(C,C')$. Here $T(C,C')$ is the set of complex matrices $(c_{nk}\equiv(a_{nk}+ib_{nk})$ satisfying the conditions $\varlimsup\limits_{n\to\infty}\sum_{k=1}^\infty|a_{nk}|=C\ge1$, $\varlimsup\limits_{n\to\infty}\sum_{k=1}^\infty|b_{nk}|=C'\ge0$.

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English version:
Mathematical Notes, 1976, 19:5, 424–429

Bibliographic databases:

UDC: 517
Received: 14.06.1975

Citation: A. A. Shcherbakov, “The kernel of a sequence obtained from a given sequence with the aid of a regular transformation”, Mat. Zametki, 19:5 (1976), 707–716; Math. Notes, 19:5 (1976), 424–429

Citation in format AMSBIB
\Bibitem{Shc76}
\by A.~A.~Shcherbakov
\paper The kernel of a~sequence obtained from a~given sequence with the aid of a~regular transformation
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 5
\pages 707--716
\mathnet{http://mi.mathnet.ru/mz7791}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=481725}
\zmath{https://zbmath.org/?q=an:0348.40003|0341.40005}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 5
\pages 424--429
\crossref{https://doi.org/10.1007/BF01142564}


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