Rocky Mountain Journal of Mathematics

Summability of subsequences of a divergent sequence

Christopher Stuart

Full-text: Open access

Abstract

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.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 1 (2014), 289-295.

Dates
First available in Project Euclid: 2 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1401740504

Digital Object Identifier
doi:10.1216/RMJ-2014-44-1-289

Mathematical Reviews number (MathSciNet)
MR3216022

Zentralblatt MATH identifier
1298.40007

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

Keywords
Regular matrices summability of subsequences

Citation

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


Export citation

References

  • C.R. Buck, A note on subsequences, Bull. Amer. Math. Soc. 49 (1943), 898–899.
  • ––––, An addendum to A note on subsequences, Proc. Amer. Math. Soc. 7 (1956), 1074–1075.
  • J. Connor, A short proof of Steinhaus' theorem on summability, The Math. Month., June–July (1985), 420–421.
  • C. Swartz, Introduction to functional analysis, Marcel Dekker, New York, 1992. {\footnotesize
  • J. Connor, A short proof of Steinhaus' theorem on summability, The Math. Month., June–July, 1985, 420–421.
  • C. Swartz, Introduction to functional analysis, Marcel Dekker, New York, 1992.}