Norm estimates for functions of non-selfadjoint operators nonregular on the convex hull of the spectrum

Norm estimates for functions of non-selfadjoint operators nonregular on the convex hull of the... AbstractWe 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 finite 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

Norm estimates for functions of non-selfadjoint operators nonregular on the convex hull of the spectrum

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Publisher
De Gruyter Open
Copyright
© by Michael Gil’
ISSN
0420-1213
eISSN
2391-4661
D.O.I.
10.1515/dema-2017-0026
Publisher site
See Article on Publisher Site

Abstract

AbstractWe 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 finite 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.

Journal

Demonstratio Mathematicade Gruyter

Published: Oct 26, 2017

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