2024/08/25 by Liao, Chenfeng, Zhu, Chaofeng
#FOS: Mathematics #Functional Analysis (math.FA) #Primary 53D12 #Secondary 58J30
paper · doi:10.48550/arxiv.2408.13837
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.