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 $x$.
Citation
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
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