Geodesic
Nonlinear $\ast $-Lie higher derivations of standard operator algebras
Communications in Mathematics, Tome 26 (2018) no. 1, pp. 15-29

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Let $\mathcal {H}$ be an infinite-dimensional complex Hilbert space and $\mathfrak {A}$~be a standard operator algebra on $\mathcal {H}$ which is closed under the adjoint operation. It is shown that every nonlinear $\ast $-Lie higher derivation $\mathcal {D}=\{{\delta _n}\}_{n\in \mathbb {N}}$ of $\mathfrak {A}$ is automatically an additive higher derivation on $\mathfrak {A}$. Moreover, $\mathcal {D}=\{{\delta _n}\}_{n\in \mathbb {N}}$ is an inner $\ast $-higher derivation.
Classification : 16W25, 46K15, 47B47
Keywords: Nonlinear $\ast $-Lie derivation; nonlinear $\ast $-Lie higher derivation; additive $\ast $-higher derivation; standard operator algebra. 
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     author = {Ashraf, Mohammad and Ali, Shakir and Wani, Bilal Ahmad},
     title = {Nonlinear $\ast ${-Lie} higher derivations of standard operator algebras},
     journal = {Communications in Mathematics},
     pages = {15--29},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {2018},
     mrnumber = {3827141},
     zbl = {1410.16038},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2018__26_1_a2/}
}
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Ashraf, Mohammad; Ali, Shakir; Wani, Bilal Ahmad. Nonlinear $\ast $-Lie higher derivations of standard operator algebras. Communications in Mathematics, Tome 26 (2018) no. 1, pp. 15-29. http://geodesic.mathdoc.fr/item/COMIM_2018__26_1_a2/