Maps Preserving Numerical Radius or Cross Norms of Products on 2×2 Matrix Algebras

张文芳; 侯晋川

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Maps Preserving Numerical Radius or Cross Norms of Products on 2×2 Matrix Algebras

更新时间：2026-09-14

- Maps Preserving Numerical Radius or Cross Norms of Products on 2×2 Matrix Algebras
- 二阶矩阵代数上保乘积数值半径或交叉范数的映射
- Vol. 30, Issue 6, Pages: 506-511(2009)
- 作者机构：
  
  太原理工大学数学系
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2009
- 稿件说明：
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张文芳, 侯晋川. Maps Preserving Numerical Radius or Cross Norms of Products on 2×2 Matrix Algebras[J]. 2009, 30(6): 506-511.
DOI：

张文芳, 侯晋川. Maps Preserving Numerical Radius or Cross Norms of Products on 2×2 Matrix Algebras[J]. 2009, 30(6): 506-511. DOI：

摘要

在空间维数大于2时相应问题研究成果的基础上

利用量子力学基本定理

即Wigner's Theorem

讨论了复二阶矩阵代数上保持矩阵乘积数值半径或交叉范数的非线性满射

获得该类映射的完整刻画和分类

从而完善了该问题的研究.

Abstract

Based on the accomplishments of corresponding issues when the space of dimension is greater than two

the paper mainly discusses nonlinear surjective maps preserving numerical radius or cross norms of matrix products on 2×2 matrix algebras.It is proved by using fundamental theorem of quantum mechanics

namely

Wigner's Theorem.All the maps are characterized completely and classified in order to improve the issues.

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references

Hou J C,Di Q H.Maps preserving numerical range of operator products[J].Proc.Amer.Math.Soc.,2006,134:1435-1446.

Zhang X L,Hou J C,He K,Maps preserving numerical radius and cross norms of operator products[J].Linear andMultilinear Algebras,2009,57(1):523-534.

Cui J L,Hou J C,Linear maps preserving the closure of numerical range on nest algebras with maximal atomic nest[J].Int.Equ.Oper.Theo.,2003,46:253-266.

Li C K,Tsing N K,Linear preservers on numericalranges,numerical radii and unitary similarity invariant norm[J].Linear and Multilinear Algebra,1992(33):63-73.

Cui J L,Hou J C,Non-linear numerical radiusisometries on atomic nest algebras and diagonal algebras[J].J.Funct.Anal.,2004,206:414-448.

Chan J T,Li C K,Sze N S,Mappings on matrices:invariance of functional values of matrix products[J].J.Austral.Math.Soc.(Serie A),2006,81:165-184.

Li C K,Sze N S.Product of operators and numerical range preserving maps[J].Studia Math.,2006,174:169-182.

Molnar L.A generalization of Wigner's unitary-antiunitary theorem to Hilbert modules[J].J.Math.Phys,1999,40:5544-5554.

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