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Algebra i Analiz, 2008, Volume 20, Issue 3, Pages 224–242 (Mi aa519)  

This article is cited in 12 scientific papers (total in 12 papers)

Research Papers

Modulus of continuity of operator functions

Yu. B. Farforovskayaa, L. Nikolskayab

a Mathematics Department, State University of Telecommunications, St. Petersburg
b Institut de Mathématiques de Bordeaux, Université Bordeaux-1, Talence, France
References:
Abstract: Let $A$ and $B$ be bounded selfadjoint operators on a separable Hilbert space, and let $f$ be a continuous function defined on an interval $[a,b]$ containing the spectra of $A$ and $B$. If $\omega _f$ denotes the modulus of continuity of $f$, then
$$ \|f(A)-f(B)\|\leq 4\Big[\log\Big(\frac{b-a}{\|A-B\|}+1\Big)+1\Big]^2\cdot\omega _f(\|A-B\|). $$
A similar result is true for unbounded selfadjoint operators, under some natural assumptions on the growth of $f$.
Keywords: Selfadjoint operator, operator function, modulas of continuity.
Received: 14.06.2007
English version:
St. Petersburg Mathematical Journal, 2009, Volume 20, Issue 3, Pages 493–506
DOI: https://doi.org/10.1090/S1061-0022-09-01058-9
Bibliographic databases:
Document Type: Article
MSC: 47B15
Language: English
Citation: Yu. B. Farforovskaya, L. Nikolskaya, “Modulus of continuity of operator functions”, Algebra i Analiz, 20:3 (2008), 224–242; St. Petersburg Math. J., 20:3 (2009), 493–506
Citation in format AMSBIB
\Bibitem{FarNik08}
\by Yu.~B.~Farforovskaya, L.~Nikolskaya
\paper Modulus of continuity of operator functions
\jour Algebra i Analiz
\yr 2008
\vol 20
\issue 3
\pages 224--242
\mathnet{http://mi.mathnet.ru/aa519}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2454458}
\zmath{https://zbmath.org/?q=an:1207.47016}
\transl
\jour St. Petersburg Math. J.
\yr 2009
\vol 20
\issue 3
\pages 493--506
\crossref{https://doi.org/10.1090/S1061-0022-09-01058-9}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000267497700009}
Linking options:
  • https://www.mathnet.ru/eng/aa519
  • https://www.mathnet.ru/eng/aa/v20/i3/p224
  • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и анализ St. Petersburg Mathematical Journal
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