<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

A note on the relationship between three classes of operators on Riesz spaces

Robert Morris University, 6001 University Blvd

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"A note on the relationship between three classes of operators on Riesz spaces"}

Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically...

A note on the relationship between three classes of operators on Riesz spaces

Published Online: Dec 21, 2020

Page range: 77 - 85

DOI: https://doi.org/10.2478/awutm-2019-0016

Keywords
Counterexamples, locally solid Riesz spaces, order bounded operators, regular operators, topologically bounded operators, topologically continuous operators

© 2019 Liang Hong, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A note on the relationship between three classes of operators on Riesz spaces

Published Online: Dec 21, 2020

Page range: 77 - 85

DOI: https://doi.org/10.2478/awutm-2019-0016

KeywordsCounterexamples, locally solid Riesz spaces, order bounded operators, regular operators, topologically bounded operators, topologically continuous operators

© 2019 Liang Hong, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Counterexamples, locally solid Riesz spaces, order bounded operators, regular operators, topologically bounded operators, topologically continuous operators