Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P. O. Box 47416-1468, Babolsar, Iran.
10.22034/kjm.2020.210055.1640
Abstract
Let $\mathcal{A}$ be a standard operator algebra on a Banach space $\mathcal{X}$ with $\dim \mathcal{X}\geq 2$. In this paper, we characterize the forms of additive maps on $\mathcal{A}$ which strongly preserve the square zero of $ \lambda $-Lie product of operators, i.e., if $\phi:\mathcal{A}\longrightarrow \mathcal{A}$ is an additive map which satisfies $$ [A,B]^2_{\lambda}=0 \Rightarrow [\phi(A),B]^2_{\lambda}=0,$$ for every $A,B \in \mathcal{A}$ and for a scalar number $\lambda$ with $\lambda \neq -1$, then it is shown that there exists a function $\sigma: \mathcal{A} \rightarrow \mathbb{C}$ such that $\phi(A)= \sigma(A) A$, for every $A \in \mathcal{A}$.
Hosseinzadeh, R. (2021). Maps strongly preserving the square zero of $ \lambda $-Lie product of operators. Khayyam Journal of Mathematics, 7(1), 109-114. doi: 10.22034/kjm.2020.210055.1640
MLA
Roja Hosseinzadeh. "Maps strongly preserving the square zero of $ \lambda $-Lie product of operators". Khayyam Journal of Mathematics, 7, 1, 2021, 109-114. doi: 10.22034/kjm.2020.210055.1640
HARVARD
Hosseinzadeh, R. (2021). 'Maps strongly preserving the square zero of $ \lambda $-Lie product of operators', Khayyam Journal of Mathematics, 7(1), pp. 109-114. doi: 10.22034/kjm.2020.210055.1640
VANCOUVER
Hosseinzadeh, R. Maps strongly preserving the square zero of $ \lambda $-Lie product of operators. Khayyam Journal of Mathematics, 2021; 7(1): 109-114. doi: 10.22034/kjm.2020.210055.1640
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