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 (formula presented) where µ is a nondecreasing function and I is the unit operator. We establish norm estimates and perturbations results for hµ(A). As particular cases the fractional powers and logarithm of A are considered.
Original language | English |
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Pages (from-to) | 607-620 |
Number of pages | 14 |
Journal | International Journal of Applied Mathematics |
Volume | 34 |
Issue number | 4 |
DOIs | |
State | Published - 1 Jan 2021 |
Keywords
- Hilbert space
- fractional power of operators
- operator logarithm Hirsch type functions
- perturbations
ASJC Scopus subject areas
- General Mathematics
- Computational Theory and Mathematics