On a Question of Bouras concerning weak compactness of almost Dunford-Pettis sets
Abstract
We give a positive answer to the question of K. Bouras [`Almost Dunford-Pettis sets in Banach lattices', Rend. Circ. Mat. Palermo (2) 62 (2013), 227--236] concerning weak compactness of almost Dunford-Pettis sets in Banach lattices. That is, every almost Dunford-Pettis set in a Banach lattice E is relatively weakly compact if, and only if, E is a KB-space.
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