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| Nonlinear Maps Preserving the Jordan Triple *-Product on Factor von Neumann Algebras |
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Citation： |
Changjing LI,Quanyuan CHEN,Ting WANG.Nonlinear Maps Preserving the Jordan Triple *-Product on Factor von Neumann Algebras[J].Chinese Annals of Mathematics B,2018,39(4):633~642 |
| Page view： 770
Net amount： 728 |
Authors： |
Changjing LI; Quanyuan CHEN;Ting WANG |
Foundation： |
The work was supported by the National Natural Science
Foundation of China (No.11526123, No.11401273) and the Natural
Science Foundation of Shandong Province of China (No.ZR2015PA010). |
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| Abstract： |
Let $\mathcal {A}$ and $\mathcal {B}$ be two factor von Neumann
algebras. For $A, B\in\mathcal {A},$ define by $[A,
B]_{*}=AB-BA^{\ast}$ the skew Lie product of $A$ and $B.$ In this article, it is proved that a bijective map $\Phi:
\mathcal {A}\rightarrow \mathcal {B}$ satisfies
$\Phi([[A,B]_{*},C]_{*})=[[\Phi(A),\Phi(B)]_{*},\Phi(C)]_{*}$ for all
$A, B,C\in\mathcal {A}$ if and only if $\Phi$ is a linear $*$-isomorphism, or a conjugate
linear $*$-isomorphism, or the negative of a linear $*$-isomorphism, or the negative of
a conjugate linear $*$-isomorphism. |
Keywords： |
Jordan triple $*$-product, Isomorphism, von Neumannalgebras |
Classification： |
47B48, 46L10 |
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