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

2025/12/03 by Li, Jinlu
#47H10 #49J52 #49J53 #90C31 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2512.04038

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.

Citations

• Covering Constants for Metric Projection Operator with Applications to Stochastic Fixed-Point Problems
• Mordukhovich derivatives of the metric projection operator in uniformly convex and uniformly smooth Banach spaces
• Coincidence Points of Parameterized Generalized Equations with Applications to Optimal Value Functions

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