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Matematicheskie Zametki, 1972, Volume 11, Issue 4, Pages 431–436 (Mi mzm9807)  

On the exactness of a theorem of Mazur and Orlicz

N. A. Davydov

Kiev State Pedagogical Institute
Abstract: For a preassigned unbounded sequence $\{S_n\}$ of complex numbers, and preassigned complex numbers $z_1$ and $z_2\ne z_1$ we consruct: 1) regular matrices $A=||a_{nk}||$ and $B=||b_{nk}||$ such that the same bounded sequences are summable by these matrices and that $\lim\limits_{n\to\infty}S_n=z_1(A)$, $\lim\limits_{n\to\infty}S_n=z_2(B)$; 2) regular matrices $A^{(1)}=||a^{(1)}_{nk}||$ and $B^{(1)}=||b^{(1)}_{nk}||$ such that $B^{(1)}\subseteq A^{(1)}$, $\lim\limits_{n\to\infty}S_n=z_1(A^{(1)})$ and $\lim\limits_{n\to\infty}S_n=z_2(B^{(1)})$. Our results show that the well known theorem of Mazur–Orlicz on the bounded consistency of two regular matrices, one of which is boundedly stronger than the other, is exact.
Received: 18.02.1971
English version:
Mathematical Notes, 1972, Volume 11, Issue 4, Pages 263–265
DOI: https://doi.org/10.1007/BF01367501
Bibliographic databases:
Document Type: Article
UDC: 513.88
Language: Russian
Citation: N. A. Davydov, “On the exactness of a theorem of Mazur and Orlicz”, Mat. Zametki, 11:4 (1972), 431–436; Math. Notes, 11:4 (1972), 263–265
Citation in format AMSBIB
\Bibitem{Dav72}
\by N.~A.~Davydov
\paper On the exactness of a theorem of Mazur and Orlicz
\jour Mat. Zametki
\yr 1972
\vol 11
\issue 4
\pages 431--436
\mathnet{http://mi.mathnet.ru/mzm9807}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=306762}
\zmath{https://zbmath.org/?q=an:0244.40004|0235.40006}
\transl
\jour Math. Notes
\yr 1972
\vol 11
\issue 4
\pages 263--265
\crossref{https://doi.org/10.1007/BF01367501}
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