Nonlinear $\ast $-derivation-type maps on sum of triple products on $\ast $-algebras
نویسندگان
1 Center for Mathematics, Computing and Cognition, Federal University of ABC, Avenida dos Estados, 5001, 09210-580, Santo Andre, Brazil
2 Center for Mathematics, Computing and Cognition, Federal University of ABC, Avenida dos Estados, 5001, 09210-580, Santo Andre, Brazil
doi
10.22075/ijnaa.2024.34391.5136چکیده
Let $\mathcal{A}$ be a unital complex $\ast $-algebra having a nontrivial projection. In this paper, we proved that every $\ast $-derivation-type map $\Phi :\mathcal{A}\rightarrow \mathcal{A}$ on sum of triple products $\alpha _{1} abc+\alpha _{2} a^{*}cb^{*}+\alpha _{3} ba^{*}c +\alpha _{4} cab^{*}+\alpha _{5} bca+\alpha _{6} cb^{*}a^{*},$ where the scalars $\{\alpha _{k}\}_{k=1}^{6}$ are rational numbers satisfying some conditions, is an additive $\ast $-derivation. Some applications of the results obtained are also presented.
