Abstract
Order continuity of the norm (resp. of linear forms) on a Banach lattice is described within the framework of the representation theory developped by Lotz [2] and Schaefer [11]. Using the structure space of a Banach lattice, new characterizations of order continuity are obtained, and known characterizations-such as the theorem of Lozanovskii [3]-are proved by mainly topological methods.
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Nagel, R.J. Ordnungsstetigkeit in Banachverbanden. Manuscripta Math 9, 9–27 (1973). https://doi.org/10.1007/BF01320666
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DOI: https://doi.org/10.1007/BF01320666