A semigroup analogue of the Fonf--Lin--Wojtaszczyk ergodic characterization of reflexive Banach spaces with a basis
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914175986434048 |
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| author | Mugnolo, Delio |
| author_facet | Mugnolo, Delio |
| contents | In analogy to a recent result by V. Fonf, M. Lin, and P. Wojtaszczyk, we prove the following characterizations of a Banach space $X$ with a basis. (i) $X$ is finite-dimensional if and only if every bounded, uniformly continuous, mean ergodic semigroup on $X$ is uniformly mean ergodic. (ii) $X$ is reflexive if and only if every bounded strongly continuous semigroup is mean ergodic if and only if every bounded uniformly continuous semigroup on $X$ is mean ergodic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01397 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A semigroup analogue of the Fonf--Lin--Wojtaszczyk ergodic characterization of reflexive Banach spaces with a basis Mugnolo, Delio Functional Analysis In analogy to a recent result by V. Fonf, M. Lin, and P. Wojtaszczyk, we prove the following characterizations of a Banach space $X$ with a basis. (i) $X$ is finite-dimensional if and only if every bounded, uniformly continuous, mean ergodic semigroup on $X$ is uniformly mean ergodic. (ii) $X$ is reflexive if and only if every bounded strongly continuous semigroup is mean ergodic if and only if every bounded uniformly continuous semigroup on $X$ is mean ergodic. |
| title | A semigroup analogue of the Fonf--Lin--Wojtaszczyk ergodic characterization of reflexive Banach spaces with a basis |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2512.01397 |