自伴算子代数上保持乘积的c-数值半径映射的刻画

Self-adjoint Operator Algebras Preserving the c-Numerical Radius Mapping of Operator Products

令Bs(H)为复Hilbert空间H上自伴的有界线性算子全体组成的实Jordan代数。给出Bs(H)上保持算子乘积c-数值半径的满射的刻画。进而对一类特殊的c,刻画了Bs(H)上保持算子乘积的c-数值域的满射。

Let Bs( H) be the real Jordan algebra of all self-adjoint operators on a complex Hilbert space H. We characterize the surjective maps preserving the cnumerical radius of products for operators in Bs( H).Further,for a special kind of c,the form of surjections preserving the c-numerical range of products for operators in Bs( H) is obtained.