保持张量积数值域的映射

王洋洋; 侯晋川; 齐霄霏

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保持张量积数值域的映射

更新时间：2026-09-14

- 保持张量积数值域的映射
- 保持张量积数值域的映射
- Issue 3, (2012)
- 作者机构：
  
  1. 太原理工大学数学学院
  2. 山西大学数学科学学院
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2012
- 稿件说明：
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王洋洋, 侯晋川, 齐霄霏. 保持张量积数值域的映射[J]. 2012, (3).
DOI：

王洋洋, 侯晋川, 齐霄霏. 保持张量积数值域的映射[J]. 2012, (3). DOI：

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.

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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