论文标题
Banach空间的投影对称张量产品中的Daugavet属性
Daugavet property in projective symmetric tensor products of Banach spaces
论文作者
论文摘要
我们表明，Banach Space $ X $的所有对称投影量张量产品都有Daugavet属性，提供$ X $具有Daugavet属性，并且$ X $是$ L_1 $ -predual（即\ $ x^*$是等于$ l_1 $ -space）或$ x $ x $ x $ x $ x $的vector-vector-vector-value l_1 $ space。在证明这一点的过程中，我们获得了许多独立利益的结果。例如，我们以$ l_1 $ - 预定符上拓扑二的极端点来表征Daugavet属性的“本地化”版本（即\ daugavet点和最近引入的$δ$ - 点），结果是$ l_1 $ libality the Offor $ l_1 $ -preduals the $ -popoint $Δ $ l_1 $ - 具有凸直径的直径为两个属性的预先属性。这些结果也适用于嵌入式的Banach空间，尤其是为代数发挥作用。接下来，我们证明Daugavet属性和多项式Daugavet属性相当于$ L_1 $ - 先生和Lipschitz功能的空间。最后，还获得了有关投影张量产品的Daugavet物业的最新结果。
We show that all the symmetric projective tensor products of a Banach space $X$ have the Daugavet property provided $X$ has the Daugavet property and either $X$ is an $L_1$-predual (i.e.\ $X^*$ is isometric to an $L_1$-space) or $X$ is a vector-valued $L_1$-space. In the process of proving it, we get a number of results of independent interest. For instance, we characterise "localised" versions of the Daugavet property (i.e.\ Daugavet points and $Δ$-points recently introduced) for $L_1$-preduals in terms of the extreme points of the topological dual, a result which allows to characterise a polyhedrality property of real $L_1$-preduals in terms of the absence of $Δ$-points and also to provide new examples of $L_1$-preduals having the convex diametral local diameter two property. These results are also applied to nicely embedded Banach spaces so, in particular, to function algebras. Next, we show that the Daugavet property and the polynomial Daugavet property are equivalent for $L_1$-preduals and for spaces of Lipschitz functions. Finally, an improvement of recent results about the Daugavet property for projective tensor products is also got.
