Mappings Preserving Sum of Products $$a\circ b-ba^{*}$$ on Factor von Neumann Algebras
| Autor: | João Carlos da Motta Ferreira, Maria das Graças Bruno Marietto |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Bulletin of the Iranian Mathematical Society. 47:679-688 |
| ISSN: | 1735-8515 1017-060X |
| DOI: | 10.1007/s41980-020-00406-5 |
| Popis: | Let $$\mathcal {A}$$ and $$\mathcal {B}$$ be two factor von Neumann algebras. In this paper, we proved that a bijective mapping $$\varPhi :\mathcal {A}\rightarrow \mathcal {B}$$ satisfies $$\varPhi (a\circ b-ba^{*})=\varPhi (a)\circ \varPhi (b)-\varPhi (b)\varPhi (a)^{*}$$ (where $$\circ $$ is the special Jordan product on $$\mathcal {A}$$ and $$\mathcal {B},$$ respectively), for all elements $$a,b\in \mathcal {A}$$ , if and only if $$\varPhi $$ is a $$*$$ -ring isomorphism. In particular, if the von Neumann algebras $$\mathcal {A}$$ and $$\mathcal {B}$$ are type I factors, then $$\varPhi $$ is a unitary isomorphism or a conjugate unitary isomorphism. |
| Databáze: | OpenAIRE |
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