Gaps and relative dimensions
Functional Analysis
2025-10-28 v3
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.
Cite
@article{arxiv.2408.13837,
title = {Gaps and relative dimensions},
author = {Chenfeng Liao and Chaofeng Zhu},
journal= {arXiv preprint arXiv:2408.13837},
year = {2025}
}
Comments
52 pages