Operator-Lipschitz estimates for the singular value functional calculus

Andersson, Fredrik; Carlsson, Marcus; Perfekt, Karl-Mikael

doi:10.1090/proc/12843

Operator-Lipschitz estimates for the singular value functional calculus

Authors: Fredrik Andersson, Marcus Carlsson and Karl-Mikael Perfekt
Journal: Proc. Amer. Math. Soc. 144 (2016), 1867-1875
MSC (2010): Primary 15A18, 15A60, 47A60; Secondary 15A16, 15A45, 47A30, 47A55, 47B10
DOI: https://doi.org/10.1090/proc/12843
Published electronically: September 11, 2015
MathSciNet review: 3460149
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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.

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