Gaps and relative dimensions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908613057970176 |
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| author | Liao, Chenfeng Zhu, Chaofeng |
| author_facet | Liao, Chenfeng Zhu, Chaofeng |
| contents | In this paper, the notion of semi-compact perturbation of a closed linear subspace is introduced. Then for a of pair of closed linear subspace of a Banach space such that one is a semi-compact perturbation of the other, it is proved that the relative dimension between them is well-defined. If the perturbation is global, the relative dimension is stable, even the perturbed pair is a semi-compact perturbed one. After that, the notion of Fredholm tuple of closed linear subspaces in a Banach space is introduced. Then the stability of the Fredholm tuple is proved. Finally the perturbed augmented Morse index is studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13837 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gaps and relative dimensions Liao, Chenfeng Zhu, Chaofeng Functional Analysis Primary 53D12, Secondary 58J30 In this paper, the notion of semi-compact perturbation of a closed linear subspace is introduced. Then for a of pair of closed linear subspace of a Banach space such that one is a semi-compact perturbation of the other, it is proved that the relative dimension between them is well-defined. If the perturbation is global, the relative dimension is stable, even the perturbed pair is a semi-compact perturbed one. After that, the notion of Fredholm tuple of closed linear subspaces in a Banach space is introduced. Then the stability of the Fredholm tuple is proved. Finally the perturbed augmented Morse index is studied. |
| title | Gaps and relative dimensions |
| topic | Functional Analysis Primary 53D12, Secondary 58J30 |
| url | https://arxiv.org/abs/2408.13837 |