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July 2016 Norm-attaining Lipschitz functionals
Vladimir Kadets, Miguel Martín, Mariia Soloviova
Banach J. Math. Anal. 10(3): 621-637 (July 2016). DOI: 10.1215/17358787-3639646

Abstract

We prove that for a given Banach space X, the subset of norm-attaining Lipschitz functionals in Lip0(X) is weakly dense but not strongly dense. Then we introduce a weaker concept of directional norm attainment and demonstrate that for a uniformly convex X the set of directionally norm-attaining Lipschitz functionals is strongly dense in Lip0(X) and, moreover, that an analogue of the Bishop–Phelps–Bollobás theorem is valid.

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Vladimir Kadets. Miguel Martín. Mariia Soloviova. "Norm-attaining Lipschitz functionals." Banach J. Math. Anal. 10 (3) 621 - 637, July 2016. https://doi.org/10.1215/17358787-3639646

Information

Received: 19 November 2015; Accepted: 28 November 2015; Published: July 2016
First available in Project Euclid: 22 August 2016

zbMATH: 1358.46009
MathSciNet: MR3541083
Digital Object Identifier: 10.1215/17358787-3639646

Subjects:
Primary: 46B04
Secondary: 46B20, 46B22, 47A30

Rights: Copyright © 2016 Tusi Mathematical Research Group

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Vol.10 • No. 3 • July 2016
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