A note on nonlinear mixed type product $[E\diamond K,D]_\ast$ on $\ast$-algebras

Year 2025, Volume: 54 Issue: 1, 16 - 25, 28.02.2025

Mohammad Aslam Siddeeque , Raof Ahmad Bhat , Mohammad Shane Alam

https://doi.org/10.15672/hujms.1294965

Abstract

Let $ \mathfrak{B}$ be a $\ast$-algebra with the unity and a nontrivial projection. In the present paper, we show under certain restrictions that if a map $\Psi$ : $ \mathfrak{B}$ $\to$ $ \mathfrak{B}$ satisfies $ \Psi ( [E \diamond K, D]_\ast ) = [\Psi( E) \diamond K, D]_\ast + [E \diamond \Psi (K), D]_\ast + [E \diamond K, \Psi (D)]_\ast$ for all $ E, K, D \in \mathfrak{B} $, then $\Psi$ is an additive $\ast$-derivation.

Keywords

*-algebra, derivation, mixed *-derivation, additivity

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