Essentially coercive forms and asympotically compact semigroups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866929306456817664 |
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| author | Arendt, W. Chalendar, I. |
| author_facet | Arendt, W. Chalendar, I. |
| contents | Form methods are most efficient to prove generation theorems for semigroups but also for proving selfadjointness. So far those theorems are based on a coercivity notion which allows the use of the Lax-Milgram Lemma. Here we consider weaker "essential" versions of coerciveness which already suffice to obtain the generator of a semigroup S or a selfadjoint operator. We also show that one of these properties, namely essentially positive coerciveness implies a very special asymptotic behaviour of S, namely asymptotic compactness; i.e. that dist(S(t),K(H)) tends to 0 as t tends to infinity, where K(H) denotes the space of all compact operators on the underlying Hilbert space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_01200 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Essentially coercive forms and asympotically compact semigroups Arendt, W. Chalendar, I. Functional Analysis 47A07, 47B44, 47A12, 47A10, 47D03 Form methods are most efficient to prove generation theorems for semigroups but also for proving selfadjointness. So far those theorems are based on a coercivity notion which allows the use of the Lax-Milgram Lemma. Here we consider weaker "essential" versions of coerciveness which already suffice to obtain the generator of a semigroup S or a selfadjoint operator. We also show that one of these properties, namely essentially positive coerciveness implies a very special asymptotic behaviour of S, namely asymptotic compactness; i.e. that dist(S(t),K(H)) tends to 0 as t tends to infinity, where K(H) denotes the space of all compact operators on the underlying Hilbert space. |
| title | Essentially coercive forms and asympotically compact semigroups |
| topic | Functional Analysis 47A07, 47B44, 47A12, 47A10, 47D03 |
| url | https://arxiv.org/abs/2002.01200 |