A characterisation of the Daugavet property in spaces of Lipschitz functions

作者：Garcia Lirola Luis; Prochazka Antonin; Rueda Zoca Abraham

来源：Journal of Mathematical Analysis and Applications, 2018, 464(1): 473-492.

DOI：10.1016/j.jmaa.2018.04.017

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

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.

• 出版日期2018-8-1