论文标题
$ \ Mathcal {l}（x）_W^*$的单位球的极端点和$ \ Mathcal {l}（x）_W $中的最佳近似值
Extreme points of the unit ball of $\mathcal{L}(X)_w^*$ and best approximation in $\mathcal{L}(X)_w$
论文作者
论文摘要
我们研究了$ \ Mathcal {l}（x）_W的几何形状，$每当数字半径定义标准时，banach space $ x上所有有界线性运算符的空间。我们获得了$ \ Mathcal {l}（x）_W。$使用此结构的双重空间的单位球的极端球的形式，我们探索Birkhoff-James的正交性，最佳近似值，最佳近似值并以$ \ Mathcal {L}（l}（x）_W。$ \ Mathcal {x）_W。$ coaste of Case of Spection Opeors Ane Andivion Andions Andivion Ane Andos Ane Ancome Andivion。最后，我们在$ \ Mathcal {l}（x）_W $中获得了Birkhoff-James正交性和$ X的等价性。$。
We study the geometry of $\mathcal{L}(X)_w,$ the space of all bounded linear operators on a Banach space $X,$ endowed with the numerical radius norm, whenever the numerical radius defines a norm. We obtain the form of the extreme points of the unit ball of the dual space of $\mathcal{L}(X)_w.$ Using this structure, we explore Birkhoff-James orthogonality, best approximation and deduce distance formula in $\mathcal{L}(X)_w.$ A special attention is given to the case of operators satisfying a notion of smoothness. Finally, we obtain an equivalence between Birkhoff-James orthogonality in $\mathcal{L}(X)_w$ and that in $X.$
