论文标题
Lipschitz功能空间中的Daugavet和Delta点
Daugavet- and Delta-points in spaces of Lipschitz functions
论文作者
论文摘要
如果单位球的每个切片分别（分别为〜包含$ x $的单位球的每个切片），则标准一个banach空间的$ x $是Daugavet点（分别为〜a $δ$ - 点），该元素几乎在$ x $中的距离为2。我们证明了在适当的度量空间上Lipschitz功能空间中Daugavet-和$δ$点的等效性，并为它们提供了两个特征。此外，我们表明，在Lipschitz功能的某些空间中，存在$δ$ - 点不是Daugavet点。最后，我们证明Lipschitz的每个空间在无限的度量空间上都包含$δ$ - 点，但可能不包含任何Daugavet点。
A norm one element $x$ of a Banach space is a Daugavet-point (respectively,~a $Δ$-point) if every slice of the unit ball (respectively,~every slice of the unit ball containing $x$) contains an element that is almost at distance 2 from $x$. We prove the equivalence of Daugavet- and $Δ$-points in spaces of Lipschitz functions over proper metric spaces and provide two characterizations for them. Furthermore, we show that in some spaces of Lipschitz functions, there exist $Δ$-points that are not Daugavet-points. Lastly, we prove that every space of Lipschitz functions over an infinite metric space contains a $Δ$-point but might not contain any Daugavet-points.
