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Izvestiya: Mathematics, 2020, Volume 84, Issue 4, Pages 659–682
DOI: https://doi.org/10.1070/IM8876
(Mi im8876)
 

This article is cited in 1 scientific paper (total in 1 paper)

Functions of perturbed pairs of non-commuting contractions

A. B. Aleksandrova, V. V. Pellerbc

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Department of Mathematics, Michigan State University, MI, USA
c Peoples' Friendship University of Russia, Moscow
References:
Abstract: We consider functions f(T,R)f(T,R) of pairs of noncommuting contractions on Hilbert space and study the problem as to which functions ff we have Lipschitz type estimates in Schatten–von Neumann norms. We prove that if ff belongs to the Besov class (B1,1)+(T2) of analytic functions in the bidisc, then we have a Lipschitz type estimate for functions f(T,R) of pairs of not necessarily commuting contractions (T,R) in the Schatten–von Neumann norms Sp for p[1,2]. On the other hand, we show that for functions in (B1,1)+(T2), there are no such Lipschitz type estimates for p>2, nor in the operator norm.
Keywords: contractions, perturbation, semi-spectral measures, Schatten–von Neumann classes, double operator integrals, triple operator integrals, Haagerup tensor products, Haagerup-like tensor products, Besov classes.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00607 А
Ministry of Education and Science of the Russian Federation 5-100
The research of the first author was partially supported by RFBR grant no. 17-01-00607A. The publication was prepared with the support of the RUDN University Program “5-100”.
Received: 25.10.2018
Revised: 04.07.2019
Bibliographic databases:
Document Type: Article
UDC: 517.983.28
Language: English
Original paper language: Russian
Citation: A. B. Aleksandrov, V. V. Peller, “Functions of perturbed pairs of non-commuting contractions”, Izv. Math., 84:4 (2020), 659–682
Citation in format AMSBIB
\Bibitem{AlePel20}
\by A.~B.~Aleksandrov, V.~V.~Peller
\paper Functions of perturbed pairs of non-commuting contractions
\jour Izv. Math.
\yr 2020
\vol 84
\issue 4
\pages 659--682
\mathnet{http://mi.mathnet.ru/eng/im8876}
\crossref{https://doi.org/10.1070/IM8876}
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\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2020IzMat..84..659A}
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Linking options:
  • https://www.mathnet.ru/eng/im8876
  • https://doi.org/10.1070/IM8876
  • https://www.mathnet.ru/eng/im/v84/i4/p41
  • This publication is cited in the following 1 articles:
    1. A. B. Aleksandrov, V. V. Peller, “Functions of perturbed commuting dissipative operators”, Math. Nachr., 295:6 (2022), 1042–1062  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:413
    Russian version PDF:48
    English version PDF:18
    References:36
    First page:8
     
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