The multiplicative norm convergence in normed Riesz algebras

Authors : Abdullah AYDIN

Pages : 24-32

Doi:10.15672/hujms.638900

View : 15 | Download : 5

Publication Date : 2021-02-04

Article Type : Research Paper

Abstract :A net $insert ignore into journalissuearticles values(x_\alpha);_{\alpha\in A}$ in an $f$-algebra $E$ is called multiplicative order convergent to $x\in E$ if $\lvert x_\alpha-x\rvert\cdot u \rightarrow 0$ for all $u\in E_+$. This convergence was introduced and studied on $f$-algebras with the order convergence. In this paper, we study a variation of this convergence for normed Riesz algebras with respect to the norm convergence. A net $insert ignore into journalissuearticles values(x_\alpha);_{\alpha\in A}$ in a normed Riesz algebra $E$ is said to be multiplicative norm convergent to $x\in E$ if $\big\lVert \lvert x_\alpha-x\rvert\cdot u\big\rVert\to 0$ for each $u\in E_+$. We study this concept and investigate its relationship with the other convergences, and also we introduce the $mn$-topology on normed Riesz algebras.
Keywords : mn convergence, normed Riesz algebra, mn topology, Riesz spaces, Riesz algebra, mo convergence