A NOTE ON NONLINEAR MIXED TYPE PRODUCT [E ⋄ K, D]∗ ON ∗-ALGEBRAS

Year 2024, Early Access, 1 - 11

Mohammad Aslam Siddeeque , Raof Ahmad Bhat , Mohammad Shane Alam

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

Abstract

Let B be a ∗-algebra with the unity and a nontrivial projection. In the present paper, we show under certain restrictions that if a map Ψ : B →B satisfies
Ψ([E ⋄ K, D]∗) = [Ψ(E) ⋄ K, D]∗ + [E ⋄Ψ(K), D]∗ + [E ⋄ K, Ψ(D)]∗ for all E, K, D ∈ B, then Ψ is an additive ∗-derivation.

Keywords

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

References

• [1] L. Dai and F. Lu, Nonlinear maps preserving Jordan ∗-products, J. Math. Anal. Appl. 409 (1), 180-188.