论文标题
在无限维空间之间定义的操作员的k平滑度的表征
Characterization of k-smoothness of operators defined between infinite-dimensional spaces
论文作者
论文摘要
我们表征了$ k-$的平滑度的平滑度，这些线性运算符在无限二维的希尔伯特空间之间定义。我们研究有限和无限二维Banach空间的问题。我们还表征了运算符在某些特定空间上的$ k-$平滑度，即$ \ mathbb {l}（\ Mathbb {x}，\ ell _ {\ ell _ {\ infty}^n），〜\ mathbb {l}（l}（\ ell _有限维的Banach空间和$ \ Mathbb {y} $是二维Banach空间。作为一个应用程序，我们表征了$ \ mathbb {l}（\ ell _ {\ infty}^3，\ mathbb {y}）的极端收缩，其中$ \ mathbb {y} $是二维多边形的Banach空间。
We characterize $k-$smoothness of bounded linear operators defined between infinite-dimensional Hilbert spaces. We study the problem in the setting of both finite and infinite-dimensional Banach spaces. We also characterize $k-$smoothness of operators on some particular spaces, namely $\mathbb{L}(\mathbb{X},\ell_{\infty}^n),~\mathbb{L}(\ell_{\infty}^3,\mathbb{Y}),$ where $\mathbb{X}$ is a finite-dimensional Banach space and $\mathbb{Y}$ is a two-dimensional Banach space. As an application, we characterize extreme contractions on $\mathbb{L}(\ell_{\infty}^3,\mathbb{Y}),$ where $\mathbb{Y}$ is a two-dimensional polygonal Banach space.
