Rocky Mountain Journal of Mathematics
- Rocky Mountain J. Math.
- Volume 44, Number 1 (2014), 289-295.
Summability of subsequences of a divergent sequence
In this paper we show that no regular matrix can sum all subsequences of a divergent sequence. We also show that the Cesaro matrix cannot sum almost all subsequences of a divergent sequence. These results can be viewed as generalizations of a well-known result of Steinhaus.
Rocky Mountain J. Math., Volume 44, Number 1 (2014), 289-295.
First available in Project Euclid: 2 June 2014
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Stuart, Christopher. Summability of subsequences of a divergent sequence. Rocky Mountain J. Math. 44 (2014), no. 1, 289--295. doi:10.1216/RMJ-2014-44-1-289. https://projecteuclid.org/euclid.rmjm/1401740504