-smoothness on polyhedral Banach spaces
Volume 169 / 2022
Colloquium Mathematicum 169 (2022), 25-37
MSC: Primary 46B20, Secondary 47L05.
DOI: 10.4064/cm8520-4-2021
Published online: 24 January 2022
Abstract
We characterize k-smoothness of an element on the unit sphere of a finite-dimensional polyhedral Banach space. Then we study k-smoothness of an operator T \in \mathbb {L}(\ell _{\infty }^n,\mathbb {Y}), where \mathbb {Y} is a two-dimensional Banach space with the additional condition that T attains its norm at each extreme point of B_{\ell _{\infty }^{n}}. We also characterize k-smoothness of an operator from \ell _{\infty }^3 to \ell _{1}^3.
