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arXiv · 1805.02034

Nonlinear maps preserving Jordan $\eta$-$\ast$-$n$-products

Wenhui Lin
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Abstract

Let $\eta\neq -1$ be a non-zero complex number, and let $\phi$ be a not necessarily linear bijection between two von Neumann algebras, one of which has no central abelian projections preserving the Jordan $\eta$-$\ast$-$n$-product. It is showed that $\phi$ is a linear $\ast$-isomorphism if $\eta$ is not real and $\phi$ is the sum of a linear $\ast$-isomorphism and a conjugate linear $\ast$-isomorphism if $\eta$ is real.

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Wenhui Lin. 2018-05-05. Nonlinear maps preserving Jordan $\eta$-$\ast$-$n$-products. https://arxiv.org/abs/1805.02034

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