Abstract

In this paper, we investigate operators on Riesz algebras, which are continuous with respect to multiplicative modifications of order convergence and relatively uniform convergence. We also introduce and study $\mathbb{mo}$-Lebesgue, $\mathbb{mo}$-$KB$, and $\mathbb{mo}$-Levi operators.

Keywords: Riesz space; relatively uniform convergence; multiplicative order convergence; $\mathbb{mo}$-continuous operator; $\mathbb{omo}$-continuous operator; Riesz algebra; $d$-algebra; $\mathbb{mo}$-bounded operator; $\mathbb{mo}$-$KB$ operator.

MSC: 46A40, 46B42, 46J40, 47B65

DOI: 10.57016/MV-R79EJZ17

Pages:  1--15