论文标题
在操作员的戴维斯 - 韦兰特外壳和规范线性空间的戴维斯 - 韦兰特指数上
On the Davis-Wielandt shell of an operator and the Davis-Wielandt index of a normed linear space
论文作者
论文摘要
我们在规范的线性空间$ \ Mathcal {x} $上研究操作员的戴维斯 - 韦兰特壳和操作员的戴维斯 - 韦兰德半径。我们表明，经过适当的修改，修改后的davis-wielandt半径在$ \ nathcal {l}（\ Mathcal {x}）$上定义了标准，该$等效于$ \ nathcal {l}（\ natercal {x}}）$。我们在某些特定的多面体Banach空间中介绍了规范线性空间的Davis-Wielandt指数，并明确计算其值。我们还提出了一种估计任何多面体巴拉奇空间的戴维斯 - 韦兰特指数的通用方法。
We study the Davis-Wielandt shell and the Davis-Wielandt radius of an operator on a normed linear space $\mathcal{X}$. We show that after a suitable modification, the modified Davis-Wielandt radius defines a norm on $\mathcal{L}(\mathcal{X})$ which is equivalent to the usual operator norm on $\mathcal{L}(\mathcal{X})$. We introduce the Davis-Wielandt index of a normed linear space and compute its value explicitly in case of some particular polyhedral Banach spaces. We also present a general method to estimate the Davis-Wielandt index of any polyhedral Banach space.
