论文标题
在操作员空间中
Frechet differentiability and quasi-polyhedrality in spaces of operators
论文作者
论文摘要
令$ x，y $为无限的尺寸，巴拉克空间。令$ \ Mathcal {l}（x，y）$为有限运算符的空间。受到这样一个事实的激励，即规范在较高的双阶空间的较高双重阶段的平稳性可能会导致特征的不同之处，我们展示了一类Banach空间$ x，y $，在紧凑的操作员$ \ nathcal {k}（x，x，x，x，y Mathc $ \ ny $ \ ythy $ \ ns $）中，非常顺利的点（即，在双层中保持光滑的点保持平稳）（y MATHC），在$ \ Mathcal {k}（x，y）$中。
Let $X, Y$ be infinite dimensional, Banach spaces. Let $\mathcal{L}(X, Y)$ be the space of bounded operators . Motivated by the fact that smoothness of norm in the higher duals of even order of a Banach space can lead to Frechet differentiability, we exhibit classes of Banach spaces $X, Y$ where very smooth points (i.e., smooth points that remain smooth in the bidual) in the space of compact operators $\mathcal{K}(X, Y)$ are Frechet smooth in $\mathcal{L}(X, Y)$ and hence in $\mathcal{K}(X, Y)$.
