论文标题
在Banach空间中的Daugavet-和Delta点，无条件的基础
Daugavet- and delta-points in Banach spaces with unconditional bases
论文作者
论文摘要
我们研究了Banach空间的单位领域的Daugavet和Delta-Points的存在，其基础为$ 1 $。如果单位球中的每个元素（分别为$ x $本身）位于单位球元件的封闭凸壳中，则标准的一个元素$ x $是Daugavet点（分别为Delta-Point），如果单位球元素在$ x $ $ x $的距离为$ 2 $。当且仅当每个标准一个元素都是Daugavet点（分别为delta-point）时，Banach空间具有Daugavet属性（分别为直径的局部直径两个属性）。众所周知，拥有Daugavet物业的Banach空间没有无条件的基础。同样，具有直径局部直径的空间两个属性也没有无条件的基础，而无条件常数严格低于$ 2 $。 我们表明，没有具有亚对称基础的BANACH空间可以具有三角点。相比之下，我们构建了一个带有$ 1 $ unconditional的Banach空间，但没有达尔塔（Delta）点，但没有Daugavet点，还有一个带有$ 1 $ unconditional的Banach空间，其单位球，其中Daugavet-Points较弱。
We study the existence of Daugavet- and delta-points in the unit sphere of Banach spaces with a $1$-unconditional basis. A norm one element $x$ in a Banach space is a Daugavet-point (resp. delta-point) if every element in the unit ball (resp. $x$ itself) is in the closed convex hull of unit ball elements that are almost at distance $2$ from $x$. A Banach space has the Daugavet property (resp. diametral local diameter two property) if and only if every norm one element is a Daugavet-point (resp. delta-point). It is well-known that a Banach space with the Daugavet property does not have an unconditional basis. Similarly spaces with the diametral local diameter two property do not have an unconditional basis with suppression unconditional constant strictly less than $2$. We show that no Banach space with a subsymmetric basis can have delta-points. In contrast we construct a Banach space with a $1$-unconditional basis with delta-points, but with no Daugavet-points, and a Banach space with a $1$-unconditional basis with a unit ball in which the Daugavet-points are weakly dense.
