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ON A QUESTION OF BOURAS CONCERNING WEAK COMPACTNESS OF ALMOST DUNFORD–PETTIS SETS
Published online by Cambridge University Press: 02 April 2015
Abstract
We give a positive answer to the question of 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 $\mathit{KB}$-space.
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- © 2015 Australian Mathematical Publishing Association Inc.
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