Yet on linear structures of norm-attaining functionals on Asplund spaces |
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Authors: | Lixin CHENG Sijie LUO |
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Affiliation: | School of Mathematical Sciences, Xiamen University, Xiamen 361005, China |
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Abstract: | 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. |
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Keywords: | norm-attaining functional Asplund space Banach lattice reflexive subspace Banach space 46B25 46B42 46E15 |
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