{"title":"On sweeping processes in Banach spaces","authors":"Youcef Askoura","doi":"10.1007/s43034-026-00515-y","DOIUrl":null,"url":null,"abstract":"<div><p>Given the real line interval <span>\\(I=[0,T]\\)</span> and a separable Banach space <i>E</i>, we consider the basic sweeping process defined by a moving set <span>\\(C:I\\rightarrow 2^E\\)</span> and add at a second time a perturbation defined by a Carathéodory integrand <span>\\(f:I\\times E\\rightarrow E\\)</span>. Assuming mainly usual assumptions and adding respectively (for the two cases) the weak compactness and the norm compactness of values of <i>C</i>, we obtain existence of solutions through an embedding of <i>E</i> in a Hilbert space. This allows to use a scalar product to perform projections. Then, describes well directed solutions with a convenient orthogonality notion, better than that represented by the (non symmetric) semi-scalar product. We adopt functions of bounded variation as solutions.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"17 3","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2026-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s43034-026-00515-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Given the real line interval \(I=[0,T]\) and a separable Banach space E, we consider the basic sweeping process defined by a moving set \(C:I\rightarrow 2^E\) and add at a second time a perturbation defined by a Carathéodory integrand \(f:I\times E\rightarrow E\). Assuming mainly usual assumptions and adding respectively (for the two cases) the weak compactness and the norm compactness of values of C, we obtain existence of solutions through an embedding of E in a Hilbert space. This allows to use a scalar product to perform projections. Then, describes well directed solutions with a convenient orthogonality notion, better than that represented by the (non symmetric) semi-scalar product. We adopt functions of bounded variation as solutions.
期刊介绍：
Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group.
Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory.
Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.
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