Volume 20, Issue 1 (4-2025)
IJMSI 2025, 20(1): 43-51 |
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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-en.html
URL: http://ijmsi.ir/article-1-1911-en.html
Abstract:
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.
Keywords: ∗-ring isomorphisms, Factor von Neumann algebras.
Type of Study: Research paper |
Subject:
General
References
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