Maps Completely Preserving Jordan 1-$*$-Zero-Product on Factor Von Neumann Algebras
Received:June 23, 2017  Revised:September 15, 2017
Key Word: factor von Neumann algebras   Jordan 1-$*$-zero-product   complete preserver problems
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11501401).
 Author Name Affiliation Li HUANG Department of Mathematics, Taiyuan University of Science and Technology, Shanxi 030024, P. R. China Yu ZHANG Department of Mathematics, Taiyuan University of Science and Technology, Shanxi 030024, P. R. China Wenhui LI Department of Mathematics, Taiyuan University of Science and Technology, Shanxi 030024, P. R. China
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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.