Charles W. Swartz
Abstract
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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.
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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.
Key concepts: Bounded inverse theorem, Mathematics, Bounded function, Bounded operator, Pointwise, Order (exchange), Uniform boundedness, Bounded deformation