Mappings preserving sum of products a◊b + b*a (resp., a*◊b + ab*) on ∗-algebras
DOI:
https://doi.org/10.22199/issn.0717-6279-5139Keywords:
∗-ring isomorphisms, prime algebras, ∗-algebrasAbstract
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.
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Copyright (c) 2023 Ali Taghavi, João Carlos Ferreira, Maria das Graças Marietto
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