Nonlinear mixed $\zeta$-Jordan triple $*$-derivations on $*$-algebras

Document Type : Original Article

Authors

Mohammad Aslam Siddeeque

Mohammad Shane Alam

Raof Ahmad Bhat

Department of Mathematics, Aligarh Muslim University, Aligarh, India

10.22034/kjm.2025.484768.3352

Abstract

Let $ \Re $ be a unital $\ast$-algebra containing a nontrivial projection‎. ‎Let $ \zeta $ be a nonzero scalar‎.  In this paper‎, ‎under some mild conditions on $\Re$‎, ‎we prove that a mapping $ \Psi:\Re\longrightarrow \Re $ satisfies \[\Psi(E\circledcirc F\circledast_\zeta G) = \Psi (E)\circledcirc F \circledast_\zeta G‎ + ‎E\circledcirc \Psi(F)\circledast_\zeta G‎ + ‎E\circledcirc F \circledast_\zeta\Psi(G),\]‎ for all $E,F,G \in\Re $ if and only if $ \Psi $ is an additive $ \ast $-derivation and $ \Psi(\zeta E)=\zeta\Psi(E)$ for all $ E\in \Re $‎.
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Keywords

∗-derivation

ζ-Jordan ∗-derivation

Mixed Jordan triple derivation

∗-algebras

Subjects

• 16 Associative rings and algebras

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