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 language | English |
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Pages (from-to) | 1063-1071 |
Number of pages | 9 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 477 |
Issue number | 2 |
DOIs | |
Publication status | Published - 15 Sept 2019 |
Keywords
- Closed convex hull
- Double sequence
- e-convergence
- Ideal cluster point
- Ideal core
- Pringsheim limit
ASJC Scopus subject areas
- Analysis
- Applied Mathematics