A note on the relationship between three classes of operators on Riesz spaces
21 gru 2020
O artykule
Data publikacji: 21 gru 2020
Zakres stron: 77 - 85
DOI: https://doi.org/10.2478/awutm-2019-0016
Słowa kluczowe
© 2019 Liang Hong, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. Our main contribution is two-folded: (i) we provide a set of counterexamples to illustrate several extant results in the literature; (ii) we give conditions for the space of order bounded operators to coincide with the space of topologically bounded operators as well as conditions for these two spaces to coincide with the space of topologically continuous operators.