Emerging notions of norm attainment for Lipschitz maps between Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:483

Article

Choi, Geunsu¹  Choi, Yun Sung¹  Martin, Miguel² 

[1] POSTECH, Dept Math, Pohang 790784, South Korea

[2] Univ Granada, Fac Ciencias, Dept Analisis Matemat, E-18071 Granada, Spain

关键词: Banach space;    Norm attainment;    Lipschitz map;    Lipschitz function;    Uniformly convex Banach space;   

DOI  :  10.1016/j.jmaa.2019.123600

来源: Elsevier

【 摘 要 】

We classify several notions of norm attaining Lipschitz maps which were introduced previously, and present the relations among them in order to verify proper inclusions. We also analyze some results for the sets of Lipschitz maps satisfying each of these properties to be dense or not in Lipo (X, Y). For instance, we characterize a Banach space Y with the Radon-NikodYm property in terms of the denseness of norm attaining Lipschitz maps with values in Y. Further, we introduce a property called the local directional Bishop-Phelps-Bollobas property for Lipschitz compact maps, which extends the one studied previously for scalar-valued functions, and provide some new positive results. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free