Positive linear relation and application to domination problem.

ABSTRACT

In this note we prove that positive multi-valued operators on Riesz spaces which are everywhere defined are always continuous. Further, we prove that the sum of two positive relations having the same null part is itself positive. This result allows us to study the domination problem in the class of positive relations.

Keywords:

• Linear relation
• positive operator
• Riesz space
• Banach lattice

2000 Mathematics Subject Classifications:

• 47A05
• 47A06
• 47B65

Acknowledgments

The author is grateful to an anonymous referee for careful corrections to and valuable comments on the original version of this paper. The author would like to thank the Deanship of Scientific Research at Majmaah University for supporting this work under Project No. R-1441-170.

Disclosure statement

No potential conflict of interest was reported by the author(s).