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arXiv · 2408.13837

Gaps and relative dimensions

Chenfeng Liao·Chaofeng Zhu
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Abstract

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.

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Chenfeng Liao, Chaofeng Zhu. 2024-08-25. Gaps and relative dimensions. https://arxiv.org/abs/2408.13837

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