International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 3, Pages 487-492

The uniform boundedness principle for order bounded operators

Charles Swartz

Department of Mathematical Sciences, New Mexico State University, Las Cruces 88003, NM, USA

Received 18 April 1988

Copyright © 1989 Charles Swartz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Under appropriate hypotheses on the spaces, it is shown that a sequence of order bounded linear operators which is pointwise order bounded is uniformly order bounded on order bounded subsets. This result is used to establish a Banach-Steinhaus Theorem for order bounded operators.