Non-global nonlinear skew Lie triple derivations on factor von Neumann algebras
Let $ \mathcal{A} $ be a factor von Neumann algebra acting on a complex Hilbert space $ H $ with dim $ \mathcal{A} > 1 $. We prove that if a map $ \delta: \mathcal{A}\rightarrow \mathcal{A} $ satisfies $ \delta([[A, B]_{\ast}, C]_{\ast}) = [[\delta(A), B]_{\ast}, C]_{\ast}+[[A, \delta(B)]_{\a...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-05-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022771?viewType=HTML |
| _version_ | 1811240126137761792 |
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| author | Liang Kong Chao Li |
| author_facet | Liang Kong Chao Li |
| author_sort | Liang Kong |
| collection | DOAJ |
| description | Let $ \mathcal{A} $ be a factor von Neumann algebra acting on a complex Hilbert space $ H $ with dim $ \mathcal{A} > 1 $. We prove that if a map $ \delta: \mathcal{A}\rightarrow \mathcal{A} $ satisfies $ \delta([[A, B]_{\ast}, C]_{\ast}) = [[\delta(A), B]_{\ast}, C]_{\ast}+[[A, \delta(B)]_{\ast}, C]_{\ast} +[[A, B]_{\ast}, \delta(C)]_{\ast} $ for any $ A, B, C\in \mathcal{A} $ with $ A^{\ast}B^{\ast}C = 0 $, then $ \delta $ is an additive $ \ast $-derivation. |
| first_indexed | 2024-04-12T13:14:59Z |
| format | Article |
| id | doaj.art-2c8108fa3eb24137aa66b1b787f05e86 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-12T13:14:59Z |
| publishDate | 2022-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-2c8108fa3eb24137aa66b1b787f05e862022-12-22T03:31:44ZengAIMS PressAIMS Mathematics2473-69882022-05-0178139631397610.3934/math.2022771Non-global nonlinear skew Lie triple derivations on factor von Neumann algebrasLiang Kong 0Chao Li 1Institute of Applied Mathematics, Shangluo University, Shangluo 726000, ChinaInstitute of Applied Mathematics, Shangluo University, Shangluo 726000, ChinaLet $ \mathcal{A} $ be a factor von Neumann algebra acting on a complex Hilbert space $ H $ with dim $ \mathcal{A} > 1 $. We prove that if a map $ \delta: \mathcal{A}\rightarrow \mathcal{A} $ satisfies $ \delta([[A, B]_{\ast}, C]_{\ast}) = [[\delta(A), B]_{\ast}, C]_{\ast}+[[A, \delta(B)]_{\ast}, C]_{\ast} +[[A, B]_{\ast}, \delta(C)]_{\ast} $ for any $ A, B, C\in \mathcal{A} $ with $ A^{\ast}B^{\ast}C = 0 $, then $ \delta $ is an additive $ \ast $-derivation.https://www.aimspress.com/article/doi/10.3934/math.2022771?viewType=HTMLnon-global nonlinear skew lie triple derivation∗-derivationfactor von neumann algebra |
| spellingShingle | Liang Kong Chao Li Non-global nonlinear skew Lie triple derivations on factor von Neumann algebras AIMS Mathematics non-global nonlinear skew lie triple derivation ∗-derivation factor von neumann algebra |
| title | Non-global nonlinear skew Lie triple derivations on factor von Neumann algebras |
| title_full | Non-global nonlinear skew Lie triple derivations on factor von Neumann algebras |
| title_fullStr | Non-global nonlinear skew Lie triple derivations on factor von Neumann algebras |
| title_full_unstemmed | Non-global nonlinear skew Lie triple derivations on factor von Neumann algebras |
| title_short | Non-global nonlinear skew Lie triple derivations on factor von Neumann algebras |
| title_sort | non global nonlinear skew lie triple derivations on factor von neumann algebras |
| topic | non-global nonlinear skew lie triple derivation ∗-derivation factor von neumann algebra |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022771?viewType=HTML |
| work_keys_str_mv | AT liangkong nonglobalnonlinearskewlietriplederivationsonfactorvonneumannalgebras AT chaoli nonglobalnonlinearskewlietriplederivationsonfactorvonneumannalgebras |