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      KCI등재 SCOPUS

      NONLINEAR MIXED ∗-JORDAN TYPE n-DERIVATIONS ON ∗-ALGEBRAS

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      https://www.riss.kr/link?id=A109061423

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      다국어 초록 (Multilingual Abstract) kakao i 다국어 번역

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      Let $ \mathfrak{R}$ be a $\ast$-algebra with unity $I$ and a nontrivial projection $P_1$. In this paper, we show that under certain restrictions if a map $ \Psi : \mathfrak{R} \to \mathfrak{R}$ satisfies \begin{align*} &\ \Psi ( S_1 \diamond S_2 \diamond \cdots \diamond S_{n-1} \bullet S_n) \\ =&\ \sum_{k = 1}^{n} S_1 \diamond S_2 \diamond \cdots \diamond S_{k-1} \diamond \Psi( S_k)\diamond S_{k+1} \diamond \cdots \diamond S_{n-1} \bullet S_n \end{align*} for all $ S_{n-2}, S_{n-1}, S_n \in \mathfrak{R} $ and $S_i=I$ for all $i \in \{1,2,\hdots, n-3\}$, where $n\geq 3$, then $ \Psi$ is an additive $\ast$-derivation.
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      Let $ \mathfrak{R}$ be a $\ast$-algebra with unity $I$ and a nontrivial projection $P_1$. In this paper, we show that under certain restrictions if a map $ \Psi : \mathfrak{R} \to \mathfrak{R}$ satisfies \begin{align*} &\ \Psi ( S_1 \diamond S_2 \diam...

      Let $ \mathfrak{R}$ be a $\ast$-algebra with unity $I$ and a nontrivial projection $P_1$. In this paper, we show that under certain restrictions if a map $ \Psi : \mathfrak{R} \to \mathfrak{R}$ satisfies \begin{align*} &\ \Psi ( S_1 \diamond S_2 \diamond \cdots \diamond S_{n-1} \bullet S_n) \\ =&\ \sum_{k = 1}^{n} S_1 \diamond S_2 \diamond \cdots \diamond S_{k-1} \diamond \Psi( S_k)\diamond S_{k+1} \diamond \cdots \diamond S_{n-1} \bullet S_n \end{align*} for all $ S_{n-2}, S_{n-1}, S_n \in \mathfrak{R} $ and $S_i=I$ for all $i \in \{1,2,\hdots, n-3\}$, where $n\geq 3$, then $ \Psi$ is an additive $\ast$-derivation.

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      참고문헌 (Reference)

      1 P. N. Anh, "Peirce decompositions, idempotents and rings" 564 : 247-275, 2020

      2 A. Taghavi, "Nonlinear ∗-Lie n-tuple derivations on prime ∗-algebras" 13 (13): 169-179, 2020

      3 C. J. Li, "Nonlinear ∗-Jordan-type derivations on ∗-algebras" 51 (51): 601-612, 2021

      4 F. F. Zhao, "Nonlinear ∗-Jordan triple derivations on von Neumann algebras" 68 (68): 163-170, 2018

      5 V. Darvish, "Nonlinear triple product A∗B+B∗A for derivations on ∗-algebras" 108 (108): 179-187, 2020

      6 C. J. Li, "Nonlinear skew Lie triple derivations between factors" 32 (32): 821-830, 2016

      7 F. J. Zhang, "Nonlinear skew Jordan derivable maps on factor von Neumann algebras" 64 (64): 2090-2103, 2016

      8 Y. Zhou, "Nonlinear mixed Lie triple derivations on prime ∗-algebras" 47 (47): 4791-4796, 2019

      9 Y. X. Liang, "Nonlinear mixed Lie triple derivable mappings on factor von Neumann algebras" 62 (62): 13-24, 2019

      10 C. J. Li, "Nonlinear mixed Jordan triple ∗-derivations on ∗-algebras" 63 (63): 735-742, 2022

      1 P. N. Anh, "Peirce decompositions, idempotents and rings" 564 : 247-275, 2020

      2 A. Taghavi, "Nonlinear ∗-Lie n-tuple derivations on prime ∗-algebras" 13 (13): 169-179, 2020

      3 C. J. Li, "Nonlinear ∗-Jordan-type derivations on ∗-algebras" 51 (51): 601-612, 2021

      4 F. F. Zhao, "Nonlinear ∗-Jordan triple derivations on von Neumann algebras" 68 (68): 163-170, 2018

      5 V. Darvish, "Nonlinear triple product A∗B+B∗A for derivations on ∗-algebras" 108 (108): 179-187, 2020

      6 C. J. Li, "Nonlinear skew Lie triple derivations between factors" 32 (32): 821-830, 2016

      7 F. J. Zhang, "Nonlinear skew Jordan derivable maps on factor von Neumann algebras" 64 (64): 2090-2103, 2016

      8 Y. Zhou, "Nonlinear mixed Lie triple derivations on prime ∗-algebras" 47 (47): 4791-4796, 2019

      9 Y. X. Liang, "Nonlinear mixed Lie triple derivable mappings on factor von Neumann algebras" 62 (62): 13-24, 2019

      10 C. J. Li, "Nonlinear mixed Jordan triple ∗-derivations on ∗-algebras" 63 (63): 735-742, 2022

      11 C. J. Li, "Nonlinear maps preserving the Jordan triple ∗-product on von Neumann algebras" 7 (7): 496-507, 2016

      12 C. J. Li, "Nonlinear maps preserving the Jordan triple ∗-product on factor von Neumann algebras" 39 (39): 633-642, 2018

      13 F. F. Zhao, "Nonlinear maps preserving the Jordan triple ∗-product between factors" 29 (29): 619-627, 2018

      14 C. J. Li, "Nonlinear maps preserving the Jordan triple 1-∗-product on von Neumann algebras" 11 (11): 109-117, 2017

      15 Z. J. Yang, "Nonlinear maps preserving mixed Lie triple products on factor von Neumann algebras" 10 (10): 325-336, 2019

      16 D. Huo, "Nonlinear mappings preserving Jordan multiple ∗-product on factor von Neumann algebras" 63 (63): 1026-1036, 2015

      17 M. A. Siddeeque, "Nonlinear bi-skew jordan derivations in prime ∗-rings" 16-, 2023

      18 A. Taghavi, "Non-linear ∗-Jordan derivations on von Neumann algebras" 64 (64): 426-439, 2016

      19 A. Taghavi, "Non-linear new product A∗B-B∗A derivations on ∗-algebras" 39 (39): 467-479, 2020

      20 B. L. M. Ferreira, "Mixed ∗-Jordan-type derivations on ∗-algebras" 22 (22): 14-, 2023

      21 Vahid Darvish ; Haji Mohammad Nazari ; Hamid Rohi ; Ali Taghavi, "Maps preserving η-product A∗B +ηBA∗ on C∗-algebras" 54 (54): 867-876, 2017

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