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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
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
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
Linking options:
https://www.mathnet.ru/eng/aa1200 https://www.mathnet.ru/eng/aa/v22/i4/p198
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Abstract page: | 448 | Full-text PDF : | 147 | References: | 45 | First page: | 8 |
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