St. Petersburg Mathematical Journal

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ISSN 1547-7371(e) ISSN 1061-0022(p)

Modulus of continuity of operator functions

Author(s): Yu. B. Farforovskaya; L. Nikolskaya
Original publication: Algebra i Analiz, tom 20 (2008), nomer 3.
Journal: St. Petersburg Math. J. 20 (2009), 493-506.
MSC (2000): Primary 47B15
Posted: April 8, 2009
MathSciNet review: 2454458
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: Let and be bounded selfadjoint operators on a separable Hilbert space, and let be a continuous function defined on an interval containing the spectra of and . If $\omega _f$ denotes the modulus of continuity of , then

$\displaystyle \Vert f(A)-f(B)\Vert \leq 4\Big[\log\Big(\frac{b-a}{\Vert A-B\Vert}+1\Big)+1\Big]^2 \cdot \omega _f(\Vert A-B\Vert).$

A similar result is true for unbounded selfadjoint operators, under some natural assumptions on the growth of

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