Rocky Mountain Journal of Mathematics

Summability of subsequences of a divergent sequence by regular matrices

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 $x$.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 2 (2018), 413-423.

Dates
First available in Project Euclid: 4 June 2018

https://projecteuclid.org/euclid.rmjm/1528077623

Digital Object Identifier
doi:10.1216/RMJ-2018-48-2-413

Mathematical Reviews number (MathSciNet)
MR3809152

Zentralblatt MATH identifier
06883473

Citation

Boos, J.; Zeltser, M. Summability of subsequences of a divergent sequence by regular matrices. Rocky Mountain J. Math. 48 (2018), no. 2, 413--423. doi:10.1216/RMJ-2018-48-2-413. https://projecteuclid.org/euclid.rmjm/1528077623

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