保持张量积数值域的映射

Maps Preserving Numerical Range of Tensor Products

提出张量积算子代数上保持简单张量积数值域的线性映射的刻画的问题.讨论了M4=M2(C)←M2(C)上保持形如A B的简单张量积的数值域的线性映射.利用二阶矩阵的特殊方法,得到了具有这种性质的线性映射具有4种不同的形式,并给出了证明梗概.同时指出有反例说明同样的刻画对于高阶情形不成立.

An open problem is proposed of characterizing the linear maps on tensor product operator algebras that preserve the numerical range of simple tensor product operators.A characterization of linear maps on M4=M2(C)←M2(C) which preserves the numerical range of simple products of the form A←B,where A,B∈M2(C),is given and an outline of the proof is presented.Ther are examples to show that the same characterization is not valid for maps on higher order.