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Abstract
We introduce and study the class of positively limited sets in Banach lattices, that is, sets on which every weak⁎ null sequence of positive functionals converges uniformly to zero. Moreover the relationships between the class of positively limited sets and other known classes of sets such as almost limited sets and (weakly) compact sets are discussed. Some properties of Banach lattices can be characterized in terms of positively limited sets.
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