@Article{CMR-31-89,
author = {Xi , Cui and JI , Guoxing},
title = {Additive Maps Preserving the Star Partial Order on $\mathcal{B}(\mathcal{H})$},
journal = {Communications in Mathematical Research },
year = {2021},
volume = {31},
number = {1},
pages = {89--96},
abstract = {<p style="text-align: justify;">Let $\mathcal{B}(\mathcal{H})$ be the $C^∗$-algebra of all bounded linear operators on a complex
Hilbert space $\mathcal{H}$. It is proved that an additive surjective map $φ$ on $\mathcal{B}(\mathcal{H})$ preserving
the star partial order in both directions if and only if one of the following assertions
holds. (1) There exist a nonzero complex number $α$ and two unitary operators <span style="text-align: justify;"></span><span style="text-align: justify;">$\boldsymbol{U}$&nbsp;and&nbsp;$\boldsymbol{V}$</span><span style="text-align: justify;"></span> on $\mathcal{H}$ such that $φ(\boldsymbol{X}) = α\boldsymbol{UXV}$&nbsp;or $φ(\boldsymbol{X}) = α\boldsymbol{UX}^∗\boldsymbol{V}$ for all $X ∈ \mathcal{B}(\mathcal{H})$. (2)
There exist a nonzero $α$ and two anti-unitary operators&nbsp;$\boldsymbol{U}$&nbsp;and&nbsp;$\boldsymbol{V}$&nbsp;on $\mathcal{H}$ such that $φ(\boldsymbol{X}) = α\boldsymbol{UXV}$ or $φ(\boldsymbol{X}) = α\boldsymbol{UX}^∗\boldsymbol{V}$ for all $X ∈ \mathcal{B}(\mathcal{H})$.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.13447/j.1674-5647.2015.01.10},
url = {http://global-sci.org/intro/article_detail/cmr/18951.html}
}