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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.13837 |
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Table of 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.