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YET ON LINEAR STRUCTURES OF NORM-ATTAINING FUNCTIONALS ON ASPLUND SPACES

YET ON LINEAR STRUCTURES OF NORM-ATTAINING FUNCTIONALS ON ASPLUND SPACES
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摘要 In this paper, we show that if an Asplund space X is either a Banach lattice or a quotient space of C（K）, then it can be equivalently renormed so that the set of norm- attaining functionals contains an infinite dimensional closed subspace of X＊ if and only if X＊ contains an infinite dimensional reflexive subspace, which gives a partial answer to a question of Bandyopadhyay and Godefroy. In this paper, we show that if an Asplund space X is either a Banach lattice or a quotient space of C（K）, then it can be equivalently renormed so that the set of norm- attaining functionals contains an infinite dimensional closed subspace of X＊ if and only if X＊ contains an infinite dimensional reflexive subspace, which gives a partial answer to a question of Bandyopadhyay and Godefroy.
作者 程立新 罗思捷
机构地区 School of Mathematical Sciences
出处 《Acta Mathematica Scientia》 SCIE CSCD 2018年第1期151-156,共6页 数学物理学报（B辑英文版）
基金 partially supported by NSFC,grant 11371296 PhD Programs Foundation of MEC,Grant 20130121110032
关键词 norm-attaining functional Asplund space Banach lattice reflexive subspace Banach space norm-attaining functional Asplund space Banach lattice reflexive subspace Banach space
分类号 O [理学]
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Acta Mathematica Scientia
2018年 第1期

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