International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 3, Pages 487-492
The uniform boundedness principle for order bounded operators
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.