International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 3, Pages 487-492
doi:10.1155/S0161171289000621

The uniform boundedness principle for order bounded operators

Abstract

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.