Near Convexity, Near Smoothness and Approximative Compactness of Half Spaces in Banach Spaces
Near Convexity, Near Smoothness and Approximative Compactness of Half Spaces in Banach Spaces
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Banach空间中半空间的近凸性、近光滑性和近似紧性
DOI：
10.1007/s10114-016-4763-5
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发表时间：
2016
影响因子：
0.7
通讯作者：
Liu Chunyan
中科院分区：
文献类型：
--
作者：
Zhang Zihou;Zhou Yu;Liu Chunyan
讨论了几乎非常凸性与性质WS的对偶关系。利用两种拟凸性和两种拟光滑性，证明了Banach空间X中的每一个半空间和对偶空间X中的每一个弱*半空间都是逼近弱紧和逼近紧的.给出了Banach空间X是Asplund空间的充分条件。利用对偶映射的上半连续性，给出了性质WS和性质S的两个刻画。
The authors discuss the dual relation of nearly very convexity and property WS. By two kinds of near convexities and two kinds of near smoothness, the authors prove a series of characterizations such that every half-space in Banach spaceXand every weak* half-space in the dual spaceX* are approximatively weakly compact and approximatively compact. They show a sufficient condition such that a Banach spaceXis a Asplund space. Using upper semi-continuity of duality mapping, the authors also give two characterizations of property WS and property S.