Rocky Mountain Journal of Mathematics

Summability of subsequences of a divergent sequence by regular matrices

J. Boos and M. Zeltser

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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

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

First available in Project Euclid: 4 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 40A05: Convergence and divergence of series and sequences 40C05: Matrix methods

Regular matrices summability of subsequences


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.

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