{"title":"On an open question concerning the domination problem in the class of almost BS-compact operators","authors":"Mohamed Hajji","doi":"10.1007/s13370-025-01300-1","DOIUrl":null,"url":null,"abstract":"<div><p>The goal of this note is to give a positive answer to the problem 4.11 in [<i>Almost BS-compact operators and domination problem, Mediterr. J. Math.</i> 18, 258 (2021)]. More precisely, we proved that if a positive operator <i>R</i> on a Banach lattice <i>E</i> is dominated by an almost <i>BS</i>-compact operator <span>\\(T: E \\rightarrow E\\)</span>, then <span>\\(R^2\\)</span> is almost <i>BS</i>-compact.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 2","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-025-01300-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The goal of this note is to give a positive answer to the problem 4.11 in [Almost BS-compact operators and domination problem, Mediterr. J. Math. 18, 258 (2021)]. More precisely, we proved that if a positive operator R on a Banach lattice E is dominated by an almost BS-compact operator \(T: E \rightarrow E\), then \(R^2\) is almost BS-compact.
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