دوره 20، شماره 1 - ( 1-1404 )
جلد 20 شماره 1 صفحات 51-43 |
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Ferreira J C D M, Marietto M D G B. Mappings Preserving Sum of Products ab + b ◦ a^∗ on Factor Von Neumann Algebras. IJMSI 2025; 20 (1) :43-51
URL: http://ijmsi.ir/article-1-1911-fa.html
URL: http://ijmsi.ir/article-1-1911-fa.html
Mappings Preserving Sum of Products ab + b ◦ a^∗ on Factor Von Neumann Algebras. مجله علوم ریاضی و انفورماتیک. 1404; 20 (1) :43-51
چکیده:
Let A and B be two factor von Neumann algebras. In this paper, we proved that a bijective mapping Φ : A → B satisfies Φ(ab+b◦a∗) = Φ(a)Φ(b)+Φ(b)◦Φ(a)∗ (where ◦ is the special Jordan product on A and B), for all elements a, b ∈ A, if and only if Φ is a ∗-ring isomorphism. In particular, if the von Neumann algebras A and B are type I factors, then Φ is a unitary isomorphism or a conjugate unitary isomorphism.
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