Turkish Journal of Mathematics
Abstract
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.
DOI
10.55730/1300-0098.3608
Keywords
Riesz space, f-algebra, order convergent net, unbounded convergent net, multiplicative order convergent net
First Page
562
Last Page
572
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
GÜRKÖK, H, & TURAN, B (2025). On multiplicative order convergence and multiplicative order continuous operators. Turkish Journal of Mathematics 49 (5): 562-572. https://doi.org/10.55730/1300-0098.3608
