The space of Pettis integrable functions is barrelled
| Autor: | Drewnoswki, Lech, Florencio Lora, Miguel, Paúl Escolano, Pedro José |
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| Přispěvatelé: | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
| Jazyk: | angličtina |
| Rok vydání: | 1992 |
| Předmět: | |
| Zdroj: | idUS. Depósito de Investigación de la Universidad de Sevilla instname |
| Popis: | It is well known that the normed space of Pettis integrable functions from a finite measure space to a Banach space is not complete in general. Here we prove that this space is always barrelled; this tells us that we may apply two important results to this space, namely, the Banach-Steinhaus uniform boundedness principle and the closed graph theorem. The proof is based on a theorem stating that a quasi-barrelled space having a convenient Boolean algebra of projections is barrelled. We also use this theorem to give similar results for the spaces of Bochner integrable functions. |
| Databáze: | OpenAIRE |
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