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arXiv · 1601.07821

Norm attaining Lipschitz functionals

Vladimir Kadets·Miguel Martin·Mariia Soloviova
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Abstract

We prove that for a given Banach space $X$, the subset of norm attaining Lipschitz functionals in $\mathrm{Lip}_0(X)$ 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 $\mathrm{Lip}_0(X)$ and, moreover, that an analogue of the Bishop-Phelps-Bollobás theorem is valid.

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BibTeXRIS

Vladimir Kadets, Miguel Martin, Mariia Soloviova. 2016-01-28. Norm attaining Lipschitz functionals. https://doi.org/10.1215/17358787-3639646

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