Abstract
The criterion of Dunford-Pettis for weak compactness in Banach lattices of L1(μ) type can be derived from a characterisation of weak sequentially complete topological vector lattices. This can be done by introducing a concept which reduces to uniform integrability in the L1(μ) case ([1], [8]). In other cases suitable choice of the topology leads to definitions given by [4], [9], [11] and [12]. It is shown in this paper that the orthogonally compact subsets of a Banach lattice are characterized as those relatively weakly compact sets on which the norm and the order topology agree.
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Der Inhalt dieser Arbeit ist ein Auszug aus der Dissertation des Autors an der Universität Dortmund
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Kühn, B. Orthogonalkompakte Teilmengen topologischer Vektorverbände. Manuscripta Math 33, 217–226 (1981). https://doi.org/10.1007/BF01798227
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DOI: https://doi.org/10.1007/BF01798227