Abstract
We consider a bounded linear operator A in a Hilbert space with a Hilbert-Schmidt Hermitian component (A A*)/2i. A sharp norm estimate is established for functions of A nonregular on the convex hull of the spectrum. The logarithm, fractional powers and meromorphic functions of operators are examples of such functions. Our results are based on the existence of a sequence An (n = 1, 2, ...) of nite dimensional operators strongly converging to A, whose spectra belongs to the spectrum of A. Besides, it is shown that the resolvents and holomorphic functions of An strongly converge to the resolvent and corresponding function of A.
Original language | English |
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Pages (from-to) | 267-277 |
Number of pages | 11 |
Journal | Demonstratio Mathematica |
Volume | 50 |
Issue number | 1 |
DOIs | |
State | Published - 1 Mar 2017 |
Keywords
- Fractional power
- Functions of non-selfadjoint operators
- Logarithm
- Meromorphic function
ASJC Scopus subject areas
- General Mathematics