Akademik Veri Yönetim Sistemi
Turkish Journal of Mathematics, cilt.49, sa.5, ss.562-572, 2025 (SCI-Expanded)
Let A and B be two f -algebras. This paper establishes the theoretical framework for multiplicative order convergence, clarifying its definition, properties, and relations to other convergence types. This includes a detailed discussion on the conditions under which multiplicative order convergence and order convergence, as well as unbounded order convergence, mutually imply each other. We establish an extension theorem for multiplicative order continuous operators, similar to Veksler’s theorem for order continuous operators. As a result of this theorem, we derive the order structure of the space of multiplicative order continuous operators. We show that the space Lmo(A, B) of order bounded unbounded multiplicative order continuous operators is an ideal in Lb(A,B) for semiprime f -algebra A and Dedekind complete f -algebra B. We also provide an example showing that Lmo(A, B) is not generally a band in Lb(A, B), and identify conditions on A or B under which it becomes one. Finally, we establish the relationships between multiplicative order continuous operators and order continuous operators.