| 保持张量积数值域的映射 |
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| 引用本文： | 王洋洋,侯晋川,齐霄霏.保持张量积数值域的映射[J].中北大学学报,2012(3):240-245. |
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| 作者姓名： | 王洋洋 侯晋川 齐霄霏 |
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| 作者单位： | 太原理工大学数学学院;山西大学数学科学学院 |
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| 基金项目： | 国家自然科学基金资助项目(11171249;11101250) |
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| 摘 要： | 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.
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| 关 键 词： | 张量积 数值域 线性映射 |
Maps Preserving Numerical Range of Tensor Products |
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| WANG Yang-yang,HOU Jin-chuan,QI Xiao-fei.Maps Preserving Numerical Range of Tensor Products[J].Journal of North University of China,2012(3):240-245. |
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| Authors: | WANG Yang-yang HOU Jin-chuan QI Xiao-fei |
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| Affiliation: | 1.College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China;2.School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China) |
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| Abstract: | 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. |
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| Keywords: | tensor product numerical range linear map |
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