Functions of noncommuting operators under perturbation of class Sp

In this article we prove that for (Formula presented.), there exist pairs of self-adjoint operators (Formula presented.) and (Formula presented.) and a function f on the real line in the homogeneous Besov class (Formula presented.) such that the differences (Formula presented.) and (Formula presented.) belong to the Schatten–von Neumann class Sp but (Formula presented.). A similar result holds for functions of contractions. We also obtain an analog of this result in the case of triples of self-adjoint operators for any (Formula presented.). © 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Authors
Aleksandrov A.B.1, 2 , Peller V.V. 3, 4
Journal
Mathematische Nachrichten
Publisher
Wiley-VCH Verlag
Number of issue
5
Language
English
Pages
847-860
Status
Published
Link
External link
DOI
10.1002/MANA.201900074
Volume
293
Year
2020
Organizations
  • 1 St. Petersburg Branch, Steklov Institute of Mathematics, Fontanka 27, St. Petersburg, 191023, Russian Federation
  • 2 St. Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, 199034, Russian Federation
  • 3 Department of Mathematics, Michigan State University, East Lansing, MI 48824, United States
  • 4 Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklay St., Moscow, 117198, Russian Federation
Keywords
46E35; 47A20; 47A55; 47A60; 47A63; Besov classes; contractions; double operator integrals; functions of noncommuting operators; Schatten–von Neumann classes; self-adjoint operators; triple operator integrals
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