Mappings preserving sum of products \(a\circ b+ba^{*}\) on factor von Neumann algebras

• Date: 2021
• Main Authors: Ferreira, J. C. M., Marietto, M. G. B.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2021
• Subjects: \(\ast\)-ring isomorphisms; factor von Neumann algebras; 47B48; 46L10
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1482
• Journal Title: Algebra and Discrete Mathematics

Let \(\mathcal{A}\) and \(\mathcal{B}\) be two factor von Neumann algebras. In this paper, we proved that a bijective mapping \(\Phi :\mathcal{A}\rightarrow \mathcal{B}\) satisfies \(\Phi (a\circ b+ba^{*})=\Phi (a)\circ \Phi (b)+\Phi (b)\Phi (a)^{*}\) (where \(\circ \) is the special Jordan product...