{"title":"On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix","authors":"S. Bouzidi, Ines Walha","doi":"10.1515/gmj-2024-2029","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we are interested to formulate new assumptions on the entries of an unbounded 3 × 3 3\\times 3 block operator matrix defined with a maximal domain on the product of Banach spaces guaranteeing its corresponding Frobenius–Schur formula. Our approach allows us to derive some original stability results intervening in the theory of perturbed lower semi-Fredholm operators involving the concept of a measure of non-strict cosingularity perturbation. A new technique is presented to investigate the Weidmann and defect essential spectra of the closure of such model of operator matrix via new criterion of perturbation.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Georgian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/gmj-2024-2029","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract In this paper, we are interested to formulate new assumptions on the entries of an unbounded 3 × 3 3\times 3 block operator matrix defined with a maximal domain on the product of Banach spaces guaranteeing its corresponding Frobenius–Schur formula. Our approach allows us to derive some original stability results intervening in the theory of perturbed lower semi-Fredholm operators involving the concept of a measure of non-strict cosingularity perturbation. A new technique is presented to investigate the Weidmann and defect essential spectra of the closure of such model of operator matrix via new criterion of perturbation.
期刊介绍:
The Georgian Mathematical Journal was founded by the Georgian National Academy of Sciences and A. Razmadze Mathematical Institute, and is jointly produced with De Gruyter. The concern of this international journal is the publication of research articles of best scientific standard in pure and applied mathematics. Special emphasis is put on the presentation of results obtained by Georgian mathematicians.