On  super weak compactness of subsets and its equivalences in Banach spaces

CHENG Li-Xin; CHENG Qing-Jin; TU Kun; ZHANG Ji-Chao

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On super weak compactness of subsets and its equivalences in Banach spaces

CHENG Li-Xin 1,CHENG Qing-Jin 1 #,TU Kun 2,ZHANG Ji-Chao 3

1.School of Mathematical Sciences, Xiamen University, Xiamen 361005

2.School of Mathematical Sciences, Yangzhou University, Yanghzou 225000

3.School of science, Hubei University of Technology, Wuhan 430068

*Correspondence author

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Funding: Specialized Research Fund for the Doctoral Program of Higher Education （No.20130121110032）

Opened online: 3 May 2017

Accepted by: none

Citation: CHENG Li-Xin,CHENG Qing-Jin,TU Kun.On super weak compactness of subsets and its equivalences in Banach spaces[OL]. [ 3 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4729884

Analogous to weak compactness of subsets of Banach spaces and to property of subsets in super reflexive spaces, the purpose of this paper is to discuss super weak compactness of both convex and nonconvex subsets in Banach spaces. As a result, this paper gives two characterizations of super weakly compact sets: The first one is Grothendiek's type theorem; the second one is James' type characterization. These are done by localizing some basic properties of ultrapowers and using some geometric procedures of Banach spaces.

Keywords:super weakly compact set; ultraproduct; Banach space

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