Near Convexity, Near Smoothness and Approximative Compactness of Half Spaces in Banach Spaces

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 characteriza- tions such that every half-space in Banach space X and every weak^＊ half-space in the dual space X^＊ are appr...

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Published inActa mathematica Sinica. English series Vol. 32; no. 5; pp. 599 - 606
Main Authors Zhang, Zi Hou, Zhou, Yu, Liu, Chun Yan
Format Journal Article
LanguageEnglish
Published Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.05.2016
Springer Nature B.V
Subjects
Approximation
Asplund空间
Banach space
Banach spaces
Convexity
Half spaces
Mapping
Mathematical models
Mathematics
Mathematics and Statistics
Smoothness
Studies
上半连续性
半空间
对偶关系
对偶空间
巴拿赫空间
平滑
逼近
approximative compactness
Property S
41A65
46B20
nearly strongly convex space
nearly very convex space
property WS
half-space
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Summary: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 characteriza- tions such that every half-space in Banach space X and every weak^＊ half-space in the dual space X^＊ are approximatively weakly compact and approximatively compact. They show a sufficient condition such that a Banach space X is a Asplund space. Using upper semi-continuity of duality mapping, the authors also give two characterizations of property WS and property S.
Bibliography: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 characteriza- tions such that every half-space in Banach space X and every weak^＊ half-space in the dual space X^＊ are approximatively weakly compact and approximatively compact. They show a sufficient condition such that a Banach space X is a Asplund space. Using upper semi-continuity of duality mapping, the authors also give two characterizations of property WS and property S.
11-2039/O1
Property S, property WS, nearly strongly convex space, nearly very convex space, half- space, approximative compactness
ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-016-4763-5