ESTIMATES FOR FRACTIONAL POWERS AND LOGARITHM
OF OPERATORS WITH HILBERT-SCHMIDT RESOLVENTS
AND PERTURBATION RESULTS
Michael Gil'
Department of Mathematics
Ben Gurion University of the Negev
P.0. Box 653, Beer-Sheva 84105, ISRAEL

Abstract

Let $A$ be a closed operator on a separable Hilbert space with the spectrum in the open right half-plane and a bounded Hermitian component, and let the resolvent of $A$ be a Hilbert-Schmidt operator. The paper deals with the function

\begin{displaymath} h_\mu(A)=\bi 0 \8 (A+tI)\mi d\mu(t), \end{displaymath}

where $\mu$ is a nondecreasing function and $I$ is the unit operator. We establish norm estimates and perturbations results for $h_\mu(A)$. As particular cases the fractional powers and logarithm of $A$ are considered.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 4
Year: 2021

DOI: 10.12732/ijam.v34i4.1

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