论文标题
直径为Lipschitz功能空间的两个特性
Diameter two properties for spaces of Lipschitz functions
论文作者
论文摘要
我们通过使用de leeuw变换来解决有关直径的两种特性的开放问题。也就是说，我们表明：直径两个特性，强直径两个特性和对称强直径的两个特性都在这些Lipschitz函数的空间中都不同； Space $ \ operatorName {Lip} _0（k_n）$具有对称强直径的两个属性，每$ n \ in \ mathbb {n} $，包括$ n = 2 $的情况；每个局部规范的Lipschitz功能都是道路点。
We solve some open problems regarding diameter two properties within the class of Banach spaces of real-valued Lipschitz functions by using the de Leeuw transform. Namely, we show that: the diameter two property, the strong diameter two property, and the symmetric strong diameter two property are all different for these spaces of Lipschitz functions; the space $\operatorname{Lip}_0(K_n)$ has the symmetric strong diameter two property for every $n\in \mathbb{N}$, including the case of $n=2$; every local norm-one Lipschitz function is a Daugavet point.
