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

doi:10.1016/S0252-9602(17)30122-4

Abstract

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 normattaining 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.

Key words: norm-attaining functional, Asplund space, Banach lattice, reflexive subspace, Banach space

Lixin CHENG, Sijie LUO. YET ON LINEAR STRUCTURES OF NORM-ATTAINING FUNCTIONALS ON ASPLUND SPACES[J].Acta mathematica scientia,Series B, 2018, 38(1): 151-156.

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