Smoothing of operator semigroups under relatively bounded perturbations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911663359262720 |
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| author | Arora, Sahiba Mui, Jonathan |
| author_facet | Arora, Sahiba Mui, Jonathan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18556 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Smoothing of operator semigroups under relatively bounded perturbations Arora, Sahiba Mui, Jonathan Analysis of PDEs Functional Analysis 34G10, 35B20, 35P05, 47A10, 47A55, 47B65, 47D06 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. |
| title | Smoothing of operator semigroups under relatively bounded perturbations |
| topic | Analysis of PDEs Functional Analysis 34G10, 35B20, 35P05, 47A10, 47A55, 47B65, 47D06 |
| url | https://arxiv.org/abs/2501.18556 |