{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/gmj-2023-2086","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let 𝒜{\mathcal{A}} be a standard operator algebra containing the identity operator I on an infinite dimensional complex Hilbert space ℋ{\mathcal{H}} which is closed under adjoint operation. Suppose that ϕ:𝒜→𝒜{\phi:\mathcal{A}\to\mathcal{A}} is the second nonlinear mixed Lie triple derivation. Then ϕ is an additive ∗{\ast}-derivation.
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