Article
The space of Pettis integrable functions is barrelled
Author/s | Drewnoswki, Lech
Florencio Lora, Miguel Paúl Escolano, Pedro José ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Publication Date | 1992 |
Deposit Date | 2021-09-13 |
Published in |
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Abstract | 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 ... 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. |
Citation | Drewnoswki, L., Florencio Lora, M. y Paúl Escolano, P.J. (1992). The space of Pettis integrable functions is barrelled. Proceedings of the American Mathematical Society, 114, 687-694. |
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