Convergent subseries of s -convergent series

Abstract

We say that an ideal has property (T) if for every -convergent series \( {\sum}_{n=1}^{\infty }{x}_n, \) there exists a set A such that Σn∈ℕ\A xn converges in the usual sense. The aim of this paper is to construct a nontrivial ideal with property (T) under the assumption that cov () = c.

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Correspondence to Ladislav Mišík.

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Mišík, L., Sleziak, M. & Tryba, J. Convergent subseries of s -convergent series. Lith Math J (2021). https://doi.org/10.1007/s10986-020-09504-7

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MSC

  • primary 40A35
  • secondary 40A05
  • 03E35

Keywords

  • ideal
  • filter
  • ideal convergence
  • property (T)
  • -convergent series
  • rapid P-points
  • semiselective ultrafilters