Smooth Functional Calculus and Spectral Theorem in Banach Spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910898705137664 |
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| author | Cedeño-Pérez, Luis A. Quevedo, Hernando |
| author_facet | Cedeño-Pérez, Luis A. Quevedo, Hernando |
| contents | The notion of projection families generalizes the classical notions of vector- and operator-valued measures. We show that projection families are general enough to extend the Spectral Theorem to Banach algebras and operators between Banach spaces. To this end, we first develop a Smooth Functional Calculus in Banach algebras using the Cauchy-Pompeiu formula, which is further extended to a Continuous Functional Calculus. We also show that these theorems are proper generalizations of the usual result for operators between Hilbert spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20725 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Smooth Functional Calculus and Spectral Theorem in Banach Spaces Cedeño-Pérez, Luis A. Quevedo, Hernando Functional Analysis Mathematical Physics The notion of projection families generalizes the classical notions of vector- and operator-valued measures. We show that projection families are general enough to extend the Spectral Theorem to Banach algebras and operators between Banach spaces. To this end, we first develop a Smooth Functional Calculus in Banach algebras using the Cauchy-Pompeiu formula, which is further extended to a Continuous Functional Calculus. We also show that these theorems are proper generalizations of the usual result for operators between Hilbert spaces. |
| title | Smooth Functional Calculus and Spectral Theorem in Banach Spaces |
| topic | Functional Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2410.20725 |