Banach lattices with the fatou property and optimal domains of kernel operators |
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| Authors: | Guillermo P. Curbera |
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| Affiliation: | a Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, Sevilla 41080, Spain
b Math.-Geogr. Fakultät, Katholische Universität Eichstätt-Ingolstadt, D-85072 Eichstätt, Germany |
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| Abstract: | New features of the Banach function space L1w(v), that is, the space of all v-scalarly integrable functions (with v any vector measure), are exposed. The Fatou property plays an essential role and leads to a new representation theorem for a large class of abstract Banach lattices. Applications are also given to the optimal domain of kernel operators taking their values in a Banach function space. |
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| Keywords: | 47B38 46E30 47G10 28B05 |
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