Research Article

Norm and relative uniform convergence

Published in: Quaestiones Mathematicae
Volume 47 , issue 11 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 2271–2282
DOI: 10.2989/16073606.2024.2365363
Author(s): Zili Chen Southwest Jiaotong University, China, Fu Zhang Southwest Jiaotong University, China,
Keywords: Primary: 46A40, Secondary: 46B42, AM-space, Carleman operator, local Egoroff property, discrete Banach lattice with order continuous norms, relative uniform convergence,
Download full text Get new issue alerts

Abstract

In this paper, we show that if H is a Dedekind complete normed Riesz space with the local Egoroff property, then H is lattice isomorphic to an ideal of an AM-space if and only if for any order bounded norm null sequence in H. Based on this, several characterizations of discrete Banach lattices with order continuous norms are provided. As an application, we find the special regulator for every relative uniform convergent sequence in discrete Banach lattices with order continuous norms.
« Characterizing some finite groups by the average order
Total coalitions in graphs »

Get new issue alerts for Quaestiones Mathematicae

CAPTCHA Reload CAPTCHA