Characterizations of the Ideal Core

2019/05/01 by Leonetti, Paolo · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN)

paper · doi:10.48550/arxiv.1905.00514

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 \x_n: 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 R^k 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.

Cited by

• On uniform summability

Related

• Rough families, cluster points, and cores
• Characterizations of Ideal Cluster Points
• Core equality of real sequences
• On the Relationship between Ideal Cluster Points and Ideal Limit Points
• Core and residual intersections of ideals