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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Operator-Lipschitz estimates for the singular value functional calculus
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by Fredrik Andersson, Marcus Carlsson and Karl-Mikael Perfekt PDF
Proc. Amer. Math. Soc. 144 (2016), 1867-1875 Request permission

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
  • 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
  • © Copyright 2015 American Mathematical Society
  • 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
  • MathSciNet review: 3460149