Mappings of âˆ—-derivation-type on sum of products aâ—¦b âˆ’ baâˆ— on âˆ—-algebras: Mappings of âˆ—-derivation-type on âˆ—-algebras

João Carlos da Motta Ferreira; Maria das Graças Bruno Marietto

doi:10.5269/bspm.63665

Mappings of âˆ—-derivation-type on sum of products aâ—¦b âˆ’ baâˆ— on âˆ—-algebras

Mappings of âˆ—-derivation-type on âˆ—-algebras

Authors

João Carlos da Motta Ferreira UFABC
Maria das Graças Bruno Marietto

DOI:

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

Abstract

Let A be a prime complex âˆ—-algebra. In this paper, we proved that every mapping Î´ : A â†’ A satisfying Î´(aâ—¦b âˆ’ baâˆ—) = Î´(a)â—¦b + aâ—¦Î´(b) âˆ’ Î´(b)aâˆ— âˆ’ bÎ´(a)âˆ— , (where â—¦ is the special Jordan product on A), for all elements a, b âˆˆ A, is an additive âˆ—-derivation.