@article{Hakami2024, 
author = {Khalil Hadi Hakami and Junaid Nisar and Kholood Alnefaie and Moin A. Ansari},
title = {Characterizing N-type derivations on standard operator algebras by local actions},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {9},
pages = {25319-25332},
keywords = {Lie derivation, Lie triple derivation, adjoint operation, standard operator algebra},
url = {https://www.sciopen.com/article/10.3934/math.20241236},
doi = {10.3934/math.20241236},
abstract = {On an infinite dimensional complex Hilbert space  H, we consider a standard operator algebra  S with an identity operator  I that is closed with respect to adjoint operation.  Pn(X1,X2,X3,…,Xn) is set of polynomials defined under indeterminates  X1,X2,⋯,Xn by  n with multiplicative Lie products with set of positive integers  N. It is shown that a map  Θ:S→S satisfying   Θ(Pn(D1,D2,D3,…,Dn))=∑i=1nPn(D1,…,Di−1,Θ(Di),Di+1,…,Dn),for any  D1,D2,D3,…,Dn∈S with  D1D2D3…Dn=0 can be represented as  d(x)+τ(x) for every  x∈S, where  d:S→S is an additive derivation with another map  τ:S→Z(S) that vanishes on each  (n−1)th commutator  Pn(D1,D2,D3,…,Dn) with  D1D2D3⋯Dn= 0.}
}