Tanise Carnieri Pierin, Ruth Nascimento Ferreira, Fernando Borges, Bruno Leonardo Macedo Ferreira
{"title":"About the additivity of a nonlinear mixed \\(*\\)-Jordan type derivation defined on an alternative \\(*\\)-algebra","authors":"Tanise Carnieri Pierin, Ruth Nascimento Ferreira, Fernando Borges, Bruno Leonardo Macedo Ferreira","doi":"10.1007/s43036-025-00424-2","DOIUrl":null,"url":null,"abstract":"<div><p>For an alternative <span>\\(*\\)</span>-algebra <i>A</i> under some additional hypothesis, we prove that a map from <i>A</i> into itself is a nonlinear mixed <span>\\(*\\)</span>-Jordan type derivation if and only is an additive <span>\\(*\\)</span>-derivation. As consequence, some results on the complex octonion algebra, associative <span>\\(*\\)</span>-algebras, and <span>\\(W^*\\)</span>-factor algebras were obtained.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-025-00424-2","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
For an alternative \(*\)-algebra A under some additional hypothesis, we prove that a map from A into itself is a nonlinear mixed \(*\)-Jordan type derivation if and only is an additive \(*\)-derivation. As consequence, some results on the complex octonion algebra, associative \(*\)-algebras, and \(W^*\)-factor algebras were obtained.
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