A NOTE ON NONLINEAR MIXED ∗-JORDAN TYPE DERIVATIONS ON ∗-ALGEBRAS

Document Type : Original Manuscript

Authors

1 Department of Mathematics Aligarh Muslim University, Aligarh India

2 Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India

10.22044/jas.2023.12763.1691

Abstract

Let S be a ∗-algebra containing the unity and a nontrivial projection. In the present paper, we show
that under certain restrictions if a map Ψ : S → S satisfies Ψ(L ⋄ N • D) = Ψ(L) ⋄ N • D + L ⋄Ψ(N) • D + L ⋄ N • Ψ(D) for all L, N, D ∈ S, then Ψ is an additive ∗-derivation.

Keywords