Characterizations of the ideal core

Paolo Leonetti

Research output: Contribution to journalArticle

Abstract

Given an ideal I on ω and a sequence x in a topological vector space, we let the I-core of x be the least closed convex set containing {xn:n∉I} for all I∈I. We show two characterizations of the I-core. This implies that the I-core of a bounded sequence in Rk is simply the convex hull of its I-cluster points. As applications, we simplify and extend several results in the context of Pringsheim-convergence and e-convergence of double sequences.

Original languageEnglish
Pages (from-to)1063-1071
Number of pages9
JournalJournal of mathematical analysis and applications
Volume477
Issue number2
DOIs
Publication statusPublished - 15 Sep 2019

Keywords

  • Closed convex hull
  • Double sequence
  • e-convergence
  • Ideal cluster point
  • Ideal core
  • Pringsheim limit

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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