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DOI: 10.46698/i3984-2243-2985-z
Automatic Boundedness of Some Operators Between Ordered and Topological Vector Spaces
Emelyanov, E. Y.
Vladikavkaz Mathematical Journal 2026. Vol. 28. Issue 1.
Abstract: Order-to-topology continuous operators and order-to-norm bounded operators have been recently studied by many authors mostly in the framework of Banach lattices. In the present note, we extend some of results obtained by these authors to the setting of operators from an ordered Banach space to a topological vector space. We present several conditions providing topological boundedness of such operators, and investigate uniform boundedness principle for collectively qualified families of operators, and establish uniform boundedness of power order-to-norm bounded operator semigroups on an ordered Banach space with a closed generating cone. We prove that every collectively order-to-topology bounded set of operators from an ordered Banach space to a topological vector space is collective ru-to-topology continuous and provide conditions under which such sets are uniformly bounded.
For citation: Emelyanov, E. Yu. Automatic Boundedness of Some Operators Between Ordered and Topological Vector Spaces, Vladikavkaz Math. J., 2026, vol. 28, no. 1, pp. 62-67. DOI 10.46698/i3984-2243-2985-z
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