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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
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
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
Linking options:
https://www.mathnet.ru/eng/aa519 https://www.mathnet.ru/eng/aa/v20/i3/p224
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