Mappings of ∗-derivation-type on sum of products a◦b − ba∗ on ∗-algebras

João Carlos da Motta Ferreira; Maria das Graças Bruno Marietto

doi:10.5269/bspm.63665

Mappings of ∗-derivation-type on sum of products a◦b − ba∗ on ∗-algebras

Mappings of ∗-derivation-type on ∗-algebras

João Carlos da Motta Ferreira UFABC
Maria das Graças Bruno Marietto

DOI: https://doi.org/10.5269/bspm.63665

Résumé

Let A be a prime complex ∗-algebra. In this paper, we proved that every mapping δ : A → A satisfying δ(a◦b − ba∗) = δ(a)◦b + a◦δ(b) − δ(b)a∗ − bδ(a)∗ , (where ◦ is the special Jordan product on A), for all elements a, b ∈ A, is an additive ∗-derivation.