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2018 Summability of subsequences of a divergent sequence by regular matrices
J. Boos, M. Zeltser
Rocky Mountain J. Math. 48(2): 413-423 (2018). DOI: 10.1216/RMJ-2018-48-2-413

Abstract

Stuart proved that the Cesaro matrix $C_1$ cannot sum almost every subsequence of a bounded divergent sequence $x$. At the end of the paper, he remarked, ``It seems likely that this proposition could be generalized for any regular matrix, but we do not have a proof of this.'' In this note, we confirm Stuart's conjecture, and we extend it to the more general case of divergent sequences $x$.

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J. Boos. M. Zeltser. "Summability of subsequences of a divergent sequence by regular matrices." Rocky Mountain J. Math. 48 (2) 413 - 423, 2018. https://doi.org/10.1216/RMJ-2018-48-2-413

Information

Published: 2018
First available in Project Euclid: 4 June 2018

zbMATH: 06883473
MathSciNet: MR3809152
Digital Object Identifier: 10.1216/RMJ-2018-48-2-413

Subjects:
Primary: 40A05, 40C05

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 2 • 2018
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