MULTIPLICATIVE ORDER CONTINUOUS OPERATORS ON RIESZ ALGEBRAS - Aydin, Abdullah; Emelyanov, Eduard; Gorokhova, Svetlana (Math Soc Serbia-Drustvo Matematicara Srbije, 2025)
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 mo-Lebesgue, mo-KB, and mo-Levi operators.
Keywords: Riesz space; relatively uniform convergence; multiplicative order convergence; rn-continuous operator; mrnm-continuous operator; Riesz algebra; d-algebra; rn-bounded operator; rny-KB operator