## Illinois Journal of Mathematics

### Maps preserving zero Jordan products on Hermitian operators

#### Abstract

Let $H$ be a separable complex Hilbert space and $B_s(H)$ the Jordan algebra of all Hermitian operators on $H$. Let $\theta:B_s(H)\to B_s(H)$ be a surjective ${\mathbb R}$-linear map which is continuous in the strong operator topology such that $\theta(x)\theta(y)+\theta(y)\theta(x)=0$ for all $x,y\in B_s(H)$ with $xy+yx=0$. We show that $\theta(x)=\lambda uxu^*$ for all $x\in B_s(H)$, where $\lambda$ is a nonzero real number and $u$ is a unitary or anti-unitary operator on $H$.

#### Article information

Source
Illinois J. Math., Volume 49, Number 2 (2005), 445-452.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138027

Digital Object Identifier
doi:10.1215/ijm/1258138027

Mathematical Reviews number (MathSciNet)
MR2164345

Zentralblatt MATH identifier
1092.47036

#### Citation

Chebotar, Mikhail A.; Ke, Wen-Fong; Lee, Pjek-Hwee. Maps preserving zero Jordan products on Hermitian operators. Illinois J. Math. 49 (2005), no. 2, 445--452. doi:10.1215/ijm/1258138027. https://projecteuclid.org/euclid.ijm/1258138027