Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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SUBSERIES CONVERGENCE AND SEQUENCE-EVALUATION CONVERGENCE

  • Cho, Min-Hyung (Department of Applied Mathematics Kum-Oh National University of Technology) ;
  • Hwang, Hong Taek (Department of Applied Mathematics Kum-Oh National University of Technology) ;
  • Yoo, Won Sok (Department of Applied Mathematics Kum-Oh National University of Technology)
  • Received : 1998.06.29
  • Published : 1998.09.15
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Abstract

We show a series of improved subseries convergence results, e.g., in a sequentially complete locally convex space X every weakly $c_0$-Cauchy series on X must be $c_0$-convergent. Thus, if X contains no copy of $c_0$, then every weakly $c_0$-Cauchy series on X must be subseries convergent.

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