ON A QUESTION OF BOURAS CONCERNING WEAK COMPACTNESS OF ALMOST DUNFORD–PETTIS SETS
ON A QUESTION OF BOURAS CONCERNING WEAK COMPACTNESS OF ALMOST DUNFORD–PETTIS SETS
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DOI：
10.1017/s0004972715000179
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发表时间：
2015-04
影响因子：
0.7
通讯作者：
Jin Xi Chen;Lei Li
中科院分区：
文献类型：
--
作者：
Jin Xi Chen;Lei Li
本文对Bouras提出的“Banach格中的Almost Dunford-Pettis集”问题给出了肯定的回答。Circ. Mat.巴勒莫（2）62（2013），227-236]关于Banach格中几乎Dunford-Pettis集的弱紧性。也就是说，Banach格$E$中的几乎Dunford-Pettis集是相对弱紧的当且仅当$E$是$\mathit{KB}$-空间。
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.