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Algebra i Analiz, 2010, Volume 22, Issue 4, Pages 198–213 (Mi aa1200)  

This article is cited in 11 scientific papers (total in 11 papers)

Research Papers

Hölder functions are operator-Hölder

L. N. Nikol'skayaa, Yu. B. Farforovskayab

a Institut de Mathématiques de Bordeaux, Université Bordeaux, Talence, France
b St. Petersburg State University of Telecommunications, St. Petersburg, Russia
References:
Abstract: Let $A$ and $B$ be selfadjoint operators in a separable Hilbert space such that $A-B$ is bounded. If a function $f$ satisfies the Hölder condition of order $\alpha$, $0<\alpha<1$, i.e., $|f(x)-f(y)|\leq L|x-y|^\alpha$, then $\|f(A)-f(B)\|\leq CL\|A-B\|^\alpha$, where $C$ is a constant, specifically, $C=2^{1-\alpha}+2\pi\sqrt 8\frac1{(1-2^{\alpha-1})^2}$. This result is a consequence of a general inequality in which the norm of $f(A)-f(B)$ is controlled in terms of the continuity modulus of $f$. Similar results are true for the quasicommutators $f(A)K-Kf(B)$, where $K$ is a bounded operator.
Keywords: operator-Hölder functions, Adamar–Schur multipliers.
Received: 01.07.2009
English version:
St. Petersburg Mathematical Journal, 2011, Volume 22, Issue 4, Pages 657–668
DOI: https://doi.org/10.1090/S1061-0022-2011-01161-6
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: L. N. Nikol'skaya, Yu. B. Farforovskaya, “Hölder functions are operator-Hölder”, Algebra i Analiz, 22:4 (2010), 198–213; St. Petersburg Math. J., 22:4 (2011), 657–668
Citation in format AMSBIB
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\by L.~N.~Nikol'skaya, Yu.~B.~Farforovskaya
\paper H\"older functions are operator-H\"older
\jour Algebra i Analiz
\yr 2010
\vol 22
\issue 4
\pages 198--213
\mathnet{http://mi.mathnet.ru/aa1200}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2768964}
\zmath{https://zbmath.org/?q=an:1228.47020}
\transl
\jour St. Petersburg Math. J.
\yr 2011
\vol 22
\issue 4
\pages 657--668
\crossref{https://doi.org/10.1090/S1061-0022-2011-01161-6}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84871371811}
Linking options:
  • https://www.mathnet.ru/eng/aa1200
  • https://www.mathnet.ru/eng/aa/v22/i4/p198
  • This publication is cited in the following 11 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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