Optimal domain of q-concave operators and vector measure representation of q-concave Banach lattices
Given a Banach space valued q-concave linear operator T defined on a σ-order continuous quasi-Banach function space, we provide a description of the optimal domain of T preserving q-concavity, that is, the largest σ-order continuous quasi-Banach function space to which T can be extended as a q-conca...
| Autores: | , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2015 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositório: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/103469 |
| Acesso em linha: | https://hdl.handle.net/11441/103469 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Banach lattices q-concave operators Quasi-Banach function spaces Vector measures defined on a δ-ring |
| Resumo: | Given a Banach space valued q-concave linear operator T defined on a σ-order continuous quasi-Banach function space, we provide a description of the optimal domain of T preserving q-concavity, that is, the largest σ-order continuous quasi-Banach function space to which T can be extended as a q-concave operator. We show in this way the existence of maximal extensions for q-concave operators. As an application, we show a representation theorem for q-concave Banach lattices through spaces of integrable functions with respect to a vector measure. This result culminates a series of representation theorems for Banach lattices using vector measures that have been obtained in the last twenty years. |
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