Differential operators on C*-algebras and applications to smooth functional calculus and Schwartz functions on the tangent groupoid
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866916377840844800 |
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| author | Mohsen, Omar |
| author_facet | Mohsen, Omar |
| contents | We introduce the notion of a differential operator on C*-algebras. This is a noncommutative analogue of a differential operator on a smooth manifold. We show that the common closed domain of all differential operators is closed under smooth functional calculus. As a corollary, we show that Schwartz functions on Connes tangent groupoid are closed under smooth functional calculus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_08670 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Differential operators on C*-algebras and applications to smooth functional calculus and Schwartz functions on the tangent groupoid Mohsen, Omar Operator Algebras K-Theory and Homology We introduce the notion of a differential operator on C*-algebras. This is a noncommutative analogue of a differential operator on a smooth manifold. We show that the common closed domain of all differential operators is closed under smooth functional calculus. As a corollary, we show that Schwartz functions on Connes tangent groupoid are closed under smooth functional calculus. |
| title | Differential operators on C*-algebras and applications to smooth functional calculus and Schwartz functions on the tangent groupoid |
| topic | Operator Algebras K-Theory and Homology |
| url | https://arxiv.org/abs/2210.08670 |