The Banach-Steinhaus Theorem for Ordered Spaces

Charles Swartz
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Charles Swartz: New Mexico State University, Department of Mathematical Sciences

A chapter in Generalized Functions, Convergence Structures, and Their Applications, 1988, pp 425-432 from Springer

Abstract: Abstract Let X and Y be vector lattices and Ti: X → Y a sequence of linear operators which are sequentially continuous with respect to relative uniform convergence. If {Tjx} is relatively uniformly convergent to Tx for each x ∈ X, under appropriate assumptions on the spaces, we show that the linear operator T is also continuous and that the {Ti} are order equicontinuous in a certain sense. We also establish an order version of the Uniform Boundedness Principle.

Date: 1988
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DOI: 10.1007/978-1-4613-1055-6_45

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