Cesaro bounded operators in Banach spaces
[EN] We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Cesaro bounded and strongly Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general. In this note, we give examples of topologically mixing (he...
| Autores: | , , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2020 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositório: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglês |
| OAI Identifier: | oai:riunet.upv.es:10251/169537 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/169537 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Cesàro bounded operators Kreiss bounded operators Mean ergodic operators Mixing MATEMATICA APLICADA |
| Resumo: | [EN] We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Cesaro bounded and strongly Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general. In this note, we give examples of topologically mixing (hence, not power bounded) absolutely Cesaro bounded operators on l(p)(N), 1 <= p < infinity, and provide examples of uniformly Kreiss bounded operators which are not absolutely Cesaro bounded. These results complement a few known examples (see [27] and [2]). We also obtain a characterization of power bounded operators which generalizes a result of Van Casteren [32]. In [2] Aleman and Suciu asked if every uniformly Kreiss bounded operator T on a Banach space satisfies that. We solve this question for Hilbert space operators and, moreover, we prove that, if T is absolutely Cesaro bounded on a Banach (Hilbert) space, then parallel to T-n parallel to = o(n) ((parallel to Tn parallel to=o(n12), respectively). As a consequence, every absolutely Cesaro bounded operator on a reflexive Banach space is mean ergodic. |
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