| Maps Completely Preserving Jordan 1-$*$-Zero-Product on Factor Von Neumann Algebras |
| Received:June 23, 2017 Revised:September 15, 2017 |
| Key Words:
factor von Neumann algebras Jordan 1-$*$-zero-product complete preserver problems
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11501401). |
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| Abstract: |
| Let $H$, $K$ be infinite dimensional complex Hilbert spaces, and $\mathcal{A}$, $\mathcal{B}$ be factor von Neumann algebras on $H$ and $K$, respectively. It is shown that every surjective map completely preserving Jordan 1-$*$-zero-product from $\mathcal{A}$ to $\mathcal{B}$ is a nonzero scalar multiple of either a linear $*$-isomorphism or a conjugate linear $*$-isomorphism. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2018.03.007 |
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