论文标题
Daugavet点和$δ$ - 无Lipschitz的空间
Daugavet points and $Δ$-points in Lipschitz-free spaces
论文作者
论文摘要
我们研究Daugavet点和$δ$ - 无Lipschitz的Banach空间。我们证明，如果$ m $是一个紧凑的公制空间，则在s _ {\ mathcal f（m）} $中的$μ\是一个道路点点，并且只有在$ b _ {\ mathcal f（m）} $的$ b _ {\ mathcal f（m）} $中没有严格小于$μ$的距离。此外，我们证明，如果$ x $和$ y $可以通过Lenght的可整流曲线连接，则可以按照我们的意愿接近$ d（x，y）$连接，则分子$ m_ {x，y} $是$Δ$ - 点。 $ m $的某些条件可以保证还可以获得先前的含义逆转。由于我们的工作，我们表明无Lipschitz的空间是Banach空间的自然例子，在那里我们可以保证存在不是Daugavet点的$δ$点。
We study Daugavet points and $Δ$-points in Lipschitz-free Banach spaces. We prove that, if $M$ is a compact metric space, then $μ\in S_{\mathcal F(M)}$ is a Daugavet point if, and only if, there is no denting point of $B_{\mathcal F(M)}$ at distance strictly smaller than two from $μ$. Moreover, we prove that if $x$ and $y$ are connectable by rectifiable curves of lenght as close to $d(x,y)$ as we wish, then the molecule $m_{x,y}$ is a $Δ$-point. Some conditions on $M$ which guarantee that the previous implication reverses are also obtained. As a consequence of our work, we show that Lipschitz-free spaces are natural examples of Banach spaces where we can guarantee the existence of $Δ$-points which are not Daugavet points.
