{"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}
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.
期刊介绍：
The Georgian Mathematical Journal was founded by the Georgian National Academy of Sciences and A. Razmadze Mathematical Institute, and is jointly produced with De Gruyter. The concern of this international journal is the publication of research articles of best scientific standard in pure and applied mathematics. Special emphasis is put on the presentation of results obtained by Georgian mathematicians.
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