Multiplicative order convergence in $f$-algebras

Year 2020, Volume: 49 Issue: 3, 998 - 1005, 02.06.2020

Abdullah Aydın

https://doi.org/10.15672/hujms.512073

Cited By: 7

Abstract

A net $(x_\alpha)$ in an $f$-algebra $E$ is said to be multiplicative order convergent to $x\in E$ if $\left|x_\alpha-x\right|u\oc 0$ for all $u\in E_+$. In this paper, we introduce the notions $mo$-convergence, $mo$-Cauchy, $mo$-complete, $mo$-continuous, and $mo$-KB-space. Moreover, we study the basic properties of these notions.

Keywords

$mo$-convergence, $f$-algebra, $mo$-KB-space, vector lattice

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