Non-linear ∗-Jordan triple derivation on prime ∗-algebras

2019/03/01 by Darvish, Vahid, Nouri, Mojtaba, Razeghi, Mehran +1
#46L10 #47B48 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1903.00451

Abstract

Let A be a prime ∗-algebra and Φ preserves triple ∗-Jordan derivation on A, that is, for every A,B ∈ A, Φ(A\diamond B \diamond C)=Φ(A)\diamond B\diamond C+A\diamond Φ(B)\diamond C+A\diamond B\diamond Φ(C) where A\diamond B = AB + BA^∗ then Φ is additive. Moreover, if Φ(αI) is self-adjoint for α∈\1,i\ then Φ is a ∗-derivation.

Related

• Non-Linear New Product A^*B-B^*A Derivations on ∗-Algebras
• Non-linear ∗-Jordan derivations on von Neumann algebras
• Nonlinear mixed Jordan triple *-derivations on *-algebras
• Nonlinear mixed Jordan triple *-derivations on factors
• Additivity of maps preserving Jordan η_∗-products on C^*-algebras