A General Theory of Operator-Valued Measures
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909842711511040 |
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| author | Cedeño-Pérez, Luis A. Quevedo, Hernando |
| author_facet | Cedeño-Pérez, Luis A. Quevedo, Hernando |
| contents | We construct a new kind of measures, called projection families, which generalize the classical notion of vector and operator-valued measures. The maximal class of reasonable functions admits an integral with respect to a projection family, where the integral is defined as an element of the second dual instead of the original space. We show that projection families possess strong enough properties to satisfy the theorems of Monotone Convergence and Dominated convergence, but are much easier to come by than the more restrictive operator-valued measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19306 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A General Theory of Operator-Valued Measures Cedeño-Pérez, Luis A. Quevedo, Hernando Functional Analysis Mathematical Physics We construct a new kind of measures, called projection families, which generalize the classical notion of vector and operator-valued measures. The maximal class of reasonable functions admits an integral with respect to a projection family, where the integral is defined as an element of the second dual instead of the original space. We show that projection families possess strong enough properties to satisfy the theorems of Monotone Convergence and Dominated convergence, but are much easier to come by than the more restrictive operator-valued measures. |
| title | A General Theory of Operator-Valued Measures |
| topic | Functional Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2410.19306 |