Differentiation and Covering Constants for Hilbert-Schmidt and Quasi-Hilbert-Schmidt Operators

Abstract

In this paper, we calculate the Frechet derivatives and Mordukhovich derivatives (or coderivatives) of Hilbert Schmidt operators on separable Hilbert spaces, by which we prove that the covering constant for Hilbert-Schmidt operators is zero. As an important class of Hilbert Schmidt operators, we study the differentiability of Hilbert Schmidt integral operators. Then, we introduce the concept of quasi-Hilbert Schmidt operators on separable Hilbert spaces. We provide an example of quasi-Hilbert Schmidt operators and find its Frechet derivatives and Mordukhovich derivatives.