Characterization of k-smoothness of operators defined between infinite-dimensional spaces

Abstract

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.

References in corpus (1)

• Characterization of extreme contractions through $k-$smoothness of operators

Cited by in corpus (3)

• Characterization of extreme contractions through $k-$smoothness of operators
• On k-smoothness of operators between Banach spaces
• On local preservation of orthogonality and its application to isometries