Norm attaining Lipschitz maps toward vectors

Abstract

We extend the recent result of G. Godefroy which concerns the existence of non-norm attaining Lipschitz maps in order to characterize the norm attainment toward vectors for Lipschitz maps in the general setting of underlying space. The main theorem of the present paper states that the existence of non-norm attaining Lipschitz maps toward vectors on a large class of metric spaces is characterized by the finite-dimensionality of range space. As an extension of his counterexample, some denseness results on norm attaining Lipschitz maps toward vectors are also shown.

13 pages

References in corpus (4)

• On strongly norm attaining Lipschitz maps
• Norm attaining Lipschitz functionals
• Emerging notions of norm attainment for Lipschitz maps between Banach spaces
• The Bishop-Phelps-Bollobás property and absolute sums