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.

Characterizations of the Ideal Core

LEONETTI P
2019

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.
https://www.sciencedirect.com/science/article/abs/pii/S0022247X19303889
Closed convex hull; Double sequence; e-convergence; Ideal cluster point; Ideal core; Pringsheim limit
Leonetti, P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2142078
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