{"title":"Maximal monotone operators with non-maximal graphical limit","authors":"Gerd Wachsmuth","doi":"10.1016/j.exco.2022.100073","DOIUrl":null,"url":null,"abstract":"<div><p>We present a counterexample showing that the graphical limit of maximally monotone operators might not be maximally monotone. We also characterize the directional differentiability of the resolvent of an operator <span><math><mi>B</mi></math></span> in terms of existence and maximal monotonicity of the proto-derivative of <span><math><mi>B</mi></math></span>.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"2 ","pages":"Article 100073"},"PeriodicalIF":0.0000,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X22000131/pdfft?md5=663e4b30d499d928ad6f94f949cd2209&pid=1-s2.0-S2666657X22000131-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Examples and Counterexamples","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666657X22000131","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We present a counterexample showing that the graphical limit of maximally monotone operators might not be maximally monotone. We also characterize the directional differentiability of the resolvent of an operator in terms of existence and maximal monotonicity of the proto-derivative of .
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