Non-linear maps on self-adjoint operators preserving numerical radius   and numerical range of Lie product
  Let $H$ be a complex separable Hilbert space of dimension $\geq 2$, ${\mathcal B}_s(H)$ the space of all self-adjoint operators on $H$. We give a complete classification of non-linear surjective maps on $\mathcal B_s(H)$ preserving respectively numerical radius and numerical range of Lie product. 
Kan He, Jinchuan Hou
math.OA