论文标题
$ \ mathbb {b}（\ ell_ \ infty^n，\ ell_1^m）$ birkhoff-james正交和几何形状的点对称性对称性
Point-wise Symmetry of Birkhoff-James Orthogonality and Geometry of $\mathbb{B}(\ell_\infty^n,\ell_1^m)$
论文作者
论文摘要
我们研究Birkhoff-James正交性的点对称性与操作员空间的几何形状$ \ Mathbb {B}（\ ell_ \ infty^n，\ ell_1^m）$之间的关系。我们表明，该空间中的任何非零左对称点都是一个平滑的点。我们还表明，对于$ n \ geq4 $，该空间的任何单位符号右对称点都是封闭的单位球的极端点。这是迈向表征这些单位球的极端点的第一步，并使用Birkhoff-James正交技术找到了Grothendieck $ g（m，n）$。
We study the relationship between the point-wise symmetry of Birkhoff-James orthogonality and the geometry of the space of operators $\mathbb{B}(\ell_\infty^n,\ell_1^m)$. We show that any non-zero left-symmetric point in this space is a smooth point. We also show that for $n\geq4$, any unit norm right-symmetric point of this space is an extreme point of the closed unit ball. This marks the first step towards characterizing the extreme points of these unit balls and finding the Grothendieck constants $G(m,n)$ using Birkhoff-James orthogonality techniques.
