Characterizations of the ideal core

Paolo Leonetti

doi:10.1016/j.jmaa.2019.05.001

Characterizations of the ideal core

Paolo Leonetti

Institut für Analysis und Zahlentheorie (5010)

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

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.

Originalsprache	englisch
Seiten (von - bis)	1063-1071
Seitenumfang	9
Fachzeitschrift	Journal of Mathematical Analysis and Applications
Jahrgang	477
Ausgabenummer	2
DOIs	https://doi.org/10.1016/j.jmaa.2019.05.001
Publikationsstatus	Veröffentlicht - 15 Sept. 2019

ASJC Scopus subject areas

Analyse
Angewandte Mathematik

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10.1016/j.jmaa.2019.05.001

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keywords = "Closed convex hull, Double sequence, e-convergence, Ideal cluster point, Ideal core, Pringsheim limit",

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AB - 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.

KW - Closed convex hull

KW - Double sequence

KW - e-convergence

KW - Ideal cluster point

KW - Ideal core

KW - Pringsheim limit

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SN - 0022-247X

VL - 477

SP - 1063

EP - 1071

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Characterizations of the ideal core

Abstract

ASJC Scopus subject areas

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