Operator-Lipschitz estimates for the singular value functional calculus

Abstract

We consider a functional calculus for compact operators, acting on the singular values rather than the spectrum, which appears frequently in applied mathematics. Necessary and sufficient conditions for this singular value functional calculus to be Lipschitz-continuous with respect to the Hilbert-Schmidt norm are given. We also provide sharp constants.

8 pages

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• Spectral Operators of Matrices

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