Fredholm complexes of Hilbert C*-modules
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908360388902912 |
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| author | Villegas-Villalpando, Brian Dungen, Koen van den |
| author_facet | Villegas-Villalpando, Brian Dungen, Koen van den |
| contents | We investigate complexes of Hilbert C*-modules, which are cochain complexes with (unbounded) regular operators between Hilbert C*-modules as differential maps. In particular, we provide various equivalent characterizations of the Fredholm property for such complexes of Hilbert C*-modules, and we define the Fredholm index taking values in the K-theory group of the C*-algebra. Among other properties of this index, we prove the stability under small or relatively compact perturbations, and we obtain alternative expressions for the index under the existence of a (weak or strong) Hodge decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07568 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fredholm complexes of Hilbert C*-modules Villegas-Villalpando, Brian Dungen, Koen van den Operator Algebras K-Theory and Homology 19K56 We investigate complexes of Hilbert C*-modules, which are cochain complexes with (unbounded) regular operators between Hilbert C*-modules as differential maps. In particular, we provide various equivalent characterizations of the Fredholm property for such complexes of Hilbert C*-modules, and we define the Fredholm index taking values in the K-theory group of the C*-algebra. Among other properties of this index, we prove the stability under small or relatively compact perturbations, and we obtain alternative expressions for the index under the existence of a (weak or strong) Hodge decomposition. |
| title | Fredholm complexes of Hilbert C*-modules |
| topic | Operator Algebras K-Theory and Homology 19K56 |
| url | https://arxiv.org/abs/2505.07568 |