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{"title":"标准算子代数上的第二类非线性混合李三元导数","authors":"Nadeem ur Rehman, Junaid Nisar, Bilal Ahmad Wani","doi":"10.1515/gmj-2023-2086","DOIUrl":null,"url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">𝒜</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2086_eq_0304.png\" /> <jats:tex-math>{\\mathcal{A}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be a standard operator algebra containing the identity operator <jats:italic>I</jats:italic> on an infinite dimensional complex Hilbert space <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">ℋ</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2086_eq_0308.png\" /> <jats:tex-math>{\\mathcal{H}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> which is closed under adjoint operation. Suppose that <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>ϕ</m:mi> <m:mo>:</m:mo> <m:mrow> <m:mi mathvariant=\"script\">𝒜</m:mi> <m:mo>→</m:mo> <m:mi mathvariant=\"script\">𝒜</m:mi> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2086_eq_0329.png\" /> <jats:tex-math>{\\phi:\\mathcal{A}\\to\\mathcal{A}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the second nonlinear mixed Lie triple derivation. Then ϕ is an additive <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mo>∗</m:mo> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2086_eq_0290.png\" /> <jats:tex-math>{\\ast}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-derivation.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The second nonlinear mixed Lie triple derivations on standard operator algebras\",\"authors\":\"Nadeem ur Rehman, Junaid Nisar, Bilal Ahmad Wani\",\"doi\":\"10.1515/gmj-2023-2086\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi mathvariant=\\\"script\\\">𝒜</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2023-2086_eq_0304.png\\\" /> <jats:tex-math>{\\\\mathcal{A}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be a standard operator algebra containing the identity operator <jats:italic>I</jats:italic> on an infinite dimensional complex Hilbert space <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi mathvariant=\\\"script\\\">ℋ</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2023-2086_eq_0308.png\\\" /> <jats:tex-math>{\\\\mathcal{H}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> which is closed under adjoint operation. Suppose that <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mrow> <m:mi>ϕ</m:mi> <m:mo>:</m:mo> <m:mrow> <m:mi mathvariant=\\\"script\\\">𝒜</m:mi> <m:mo>→</m:mo> <m:mi mathvariant=\\\"script\\\">𝒜</m:mi> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2023-2086_eq_0329.png\\\" /> <jats:tex-math>{\\\\phi:\\\\mathcal{A}\\\\to\\\\mathcal{A}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the second nonlinear mixed Lie triple derivation. Then ϕ is an additive <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mo>∗</m:mo> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2023-2086_eq_0290.png\\\" /> <jats:tex-math>{\\\\ast}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-derivation.\",\"PeriodicalId\":55101,\"journal\":{\"name\":\"Georgian Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-11-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Georgian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/gmj-2023-2086\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Georgian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/gmj-2023-2086","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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