A. J. O. Andrade, Gabriela C. Moraes, R. N. Ferreira, B. Ferreira
{"title":"可替换*-代数上的非线性*-Jordan型导子","authors":"A. J. O. Andrade, Gabriela C. Moraes, R. N. Ferreira, B. Ferreira","doi":"10.33048/semi.2022.19.012","DOIUrl":null,"url":null,"abstract":"Let $A$ be an unital alternative $*$-algebra. Assume that $A$ contains a nontrivial symmetric idempotent element $e$ which satisfies $xA \\cdot e = 0$ implies $x = 0$ and $xA \\cdot (1_A - e) = 0$ implies $x = 0$. In this paper, it is shown that $\\Phi$ is a nonlinear $*$-Jordan-type derivation on A if and only if $\\Phi$ is an additive $*$-derivation. As application, we get a result on alternative $W^{*}$-algebras.","PeriodicalId":45858,"journal":{"name":"Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2021-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Nonlinear *-Jordan-type derivations on alternative *-algebras\",\"authors\":\"A. J. O. Andrade, Gabriela C. Moraes, R. N. Ferreira, B. Ferreira\",\"doi\":\"10.33048/semi.2022.19.012\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $A$ be an unital alternative $*$-algebra. Assume that $A$ contains a nontrivial symmetric idempotent element $e$ which satisfies $xA \\\\cdot e = 0$ implies $x = 0$ and $xA \\\\cdot (1_A - e) = 0$ implies $x = 0$. In this paper, it is shown that $\\\\Phi$ is a nonlinear $*$-Jordan-type derivation on A if and only if $\\\\Phi$ is an additive $*$-derivation. As application, we get a result on alternative $W^{*}$-algebras.\",\"PeriodicalId\":45858,\"journal\":{\"name\":\"Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-04-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33048/semi.2022.19.012\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33048/semi.2022.19.012","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Nonlinear *-Jordan-type derivations on alternative *-algebras
Let $A$ be an unital alternative $*$-algebra. Assume that $A$ contains a nontrivial symmetric idempotent element $e$ which satisfies $xA \cdot e = 0$ implies $x = 0$ and $xA \cdot (1_A - e) = 0$ implies $x = 0$. In this paper, it is shown that $\Phi$ is a nonlinear $*$-Jordan-type derivation on A if and only if $\Phi$ is an additive $*$-derivation. As application, we get a result on alternative $W^{*}$-algebras.