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

Abstract

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 where is a finite-dimensional Banach space and is a two-dimensional Banach space. As an application, we characterize extreme contractions on where is a two-dimensional polygonal Banach space.