{"title":"Gaps and relative dimensions","authors":"Chenfeng Liao, Chaofeng Zhu","doi":"arxiv-2408.13837","DOIUrl":null,"url":null,"abstract":"In this paper, the notion of Fredholm tetrad of closed linear subspaces in a\nBanach space is introduced. Then the stability of the Fredholm tetrad is\nproved. After that, the notion of semi-compact perturbation of a closed linear\nsubspace is introduced. Then for a of pair of closed linear subspace of a\nBanach space such that one is a semi-compact perturbation of the other, it is\nproved that the relative dimension between them is well-defined. If the\nperturbation is compact, the relative dimension is stable. Finally the\nperturbed argumented Morse index is studied.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"31 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.13837","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, the notion of Fredholm tetrad of closed linear subspaces in a
Banach space is introduced. Then the stability of the Fredholm tetrad is
proved. After that, 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 compact, the relative dimension is stable. Finally the
perturbed argumented Morse index is studied.
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