A characterisation of the Daugavet property in spaces of Lipschitz functions

被引：36

作者：

Garcia-Lirola, Luis ^{[1
]}

Prochazka, Antonin ^{[2
]}

Rueda Zoca, Abraham ^{[3
]}

机构：

[1] Univ Murcia, Dept Matemat, Fac Matemat, E-30100 Murcia, Spain

[2] Univ Bourgogne Franche Comte, Lab Mathemat, UMR 6623, 16 Route Gray, F-25030 Besancon, France

[3] Univ Granada, Fac Ciencias, Dept Anal Matemat, E-18071 Granada, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 464卷 / 01期

关键词：

Daugavet property; Space of Lipschitz functions; Lipschitz-free space; Length space; Strongly exposed point;

D O I：

10.1016/j.jmaa.2018.04.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Daugavet property in the space of Lipschitz functions Lip(0)(M) on a complete metric space M. Namely we show that Lip(0)(M) has the Daugavet property if and only if M is a length metric space. This condition also characterises the Daugavet property in the Lipschitz free space F(M). Moreover, when M is compact, we show that either F(M) has the Daugavet property or its unit ball has a strongly exposed point. If M is an infinite compact subset of a strictly convex Banach space then the Daugavet property of Lip(0)(M) is equivalent to the convexity of M. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：473 / 492

页数：20

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