Smoothing of operator semigroups under relatively bounded perturbations
Abstract
We investigate a smoothing property for strongly-continuous operator semigroups, akin to ultracontractivity in parabolic evolution equations. Specifically, we establish the stability of this property under certain relatively bounded perturbations of the semigroup generator. This result yields a spectral perturbation theorem, which has implications for the long-term dynamics of evolution equations driven by elliptic operators of second and higher orders. In particular, a new perturbation theorem for so-called eventually positive semigroups is derived as a consequence of the general results.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Advanced Mathematical Modeling in Engineering
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Journal of Mathematical Analysis and Applications
- Volume
- 563
- Issue
- 1
- Pages
- 130640–130640
- Publication date
- 27 March 2026
- Language
- EN