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.
- Hilbert space
- fractional power of operators
- operator logarithm Hirsch type functions
ASJC Scopus subject areas
- Mathematics (all)
- Computational Theory and Mathematics