Mappings preserving sum of products a◊b + b*a (resp., a*◊b + ab*) on ∗-algebras

• Taghavi, Ali ^[1] ; Ferreira, João Carlos ^[2] ; Marietto, Maria das Graças
  1. [1] University of Mazandaran

     University of Mazandaran

     Irán

     
  2. [2] Universidade Federal do ABC

     Universidade Federal do ABC

     Brasil

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 42, Nº. 1, 2023, págs. 18-31
• Idioma: inglés
• Enlaces
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• Resumen

  • Let A and B be two prime complex ∗-algebras. We proved that every bijective mapping Φ : A → B satisfying Φ(a ◊+ b∗ a) = Φ(a)◊Φ(b) + Φ(b)∗Φ(a) (resp., Φ(a∗ ◊b + ab∗) = Φ(a)∗ ◊Φ(b) + Φ(a)Φ(b)∗), where a ◊b = ab + ba∗, for all elements a, b ∈ A, is a ∗-ring isomorphism.