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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)

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Dissipative operators and operator Lipschitz functions
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by A. B. Aleksandrov and V. V. Peller PDF
Proc. Amer. Math. Soc. 147 (2019), 2081-2093 Request permission

Abstract:

The purpose of this paper is to obtain an integral representation for the difference $f(L_1)-f(L_2)$ of functions of maximal dissipative operators. This representation in terms of double operator integrals will allow us to establish Lipschitz-type estimates for functions of maximal dissipative operators. We also consider a similar problem for quasicommutators, i.e., operators of the form $f(L_1)R-Rf(L_2)$.
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Additional Information
  • A. B. Aleksandrov
  • Affiliation: St. Petersburg Branch, Steklov Institute of Mathematics, Fontanka 27, 191023, St. Petersburg, Russia
  • MR Author ID: 195855
  • V. V. Peller
  • Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824 –and– People’s Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow, 117198, Russian Federation
  • MR Author ID: 194673
  • Email: peller@math.msu.edu
  • Received by editor(s): February 26, 2018
  • Received by editor(s) in revised form: July 25, 2018
  • Published electronically: February 6, 2019
  • Additional Notes: This paper was prepared under the support of the program of the Presidium of the RAS No01 “Fundamental Mathematics and its Applications” (grant PRAS-18-01).
    The research of the first author was also supported by RFBR grant 17-01-00607.
    This publication was prepared with the support of the “RUDN University Program 5-100”.
    The second author is the corresponding author.
  • Communicated by: Stephan Ramon Garcia
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 2081-2093
  • MSC (2010): Primary 47A55, 47B44; Secondary 47A63, 47A60
  • DOI: https://doi.org/10.1090/proc/14335
  • MathSciNet review: 3937684