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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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Additional Information

Fredrik Andersson
Affiliation: Centre for Mathematical Sciences, Lund University, 22100 Lund, Sweden
Email: fa@maths.lth.se

Marcus Carlsson
Affiliation: Centre for Mathematical Sciences, Lund University, 22100 Lund, Sweden
Email: marcus.carlsson@math.lu.se

Karl-Mikael Perfekt
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
Email: karl-mikael.perfekt@math.ntnu.no

DOI: https://doi.org/10.1090/proc/12843
Keywords: Lipschitz estimates, functional calculus, singular values, doubly substochastic matrices
Received by editor(s): March 16, 2015
Received by editor(s) in revised form: May 16, 2015
Published electronically: September 11, 2015
Communicated by: Pamela B. Gorkin
Article copyright: © Copyright 2015 American Mathematical Society