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二阶矩阵代数上保乘积数值半径或交叉范数的映射 被引量：2

Maps Preserving Numerical Radius or Cross Norms of Products on 2×2 Matrix Algebras
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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. 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.
作者 张文芳 侯晋川
机构地区 太原理工大学数学系
出处 《中北大学学报（自然科学版）》 CAS 北大核心 2009年第6期506-511,共6页 Journal of North University of China(Natural Science Edition)
关键词 矩阵代数 映射 数值半径 交叉范数 matrix algebra map numerical radius cross norms
分类号 O177.1 [理学—基础数学]
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参考文献8

  • 1Hou J C, Di Q H. Maps preserving numerical range of operator products[J]. Proc. Amer. Math. Soc. , 2006, 134:1435-1446.
  • 2Zhang X L, Hou J C, He K, Maps preserving numerical radius and cross norms of operator products[J]. Linear and Multitinear Algebras, 2009,57 (1):523-534.
  • 3Cui 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.
  • 4Li 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.
  • 5Cui J L, Hou J C, Non-linear numerical radiusisometries on atomic nest algebras and diagonal algebras[J]. J. Funct. Anal. , 2004, 206: 414-448.
  • 6Chan 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.
  • 7Li C K, Sze N S. Product of operators and numerical range preserving maps[J]. Studia Math. , 2006, 174: 169-182.
  • 8Molnar L. A generalization of Wigner's unitary-antiunitary theorem to Hilbert modules[J]. J. Math. Phys, 1999, 40:5544 5554.

同被引文献16

  • 1Hou J C, He K, Zhang X L. Maps preserving numerical radius or cross norms of products of self-adjoint operators[ J ]. Acta Math Sinica, to appear.
  • 2Hou J C, He K, Zhang X L. Nonlinear maps preserving numerical radius of indefinite skew product of operators [ J ]. Lin Alg Appl, 2009,430: 2240 - 2253.
  • 3Cui 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.
  • 4Cui J L, Hou J C. Non-linear numerical radius isometries on atomic nest algebras and diagonal algebras [ J ]. J Funct Anal, 2004, 206:414- 448.
  • 5Li C K, Sze N S. Product of operators and numerical range preserving maps [ J ]. Studia Math, 2006,174:169 - 182.
  • 6Hou J C, Di Q H. Maps preserving numerical range of operator products[ J ]. Proc Amer Math Soc, 2006,134:1435 - 1446.
  • 7Zhang X L, Hou J C, He K. Maps preserving numerical radius and cross norms of operator products[ J]. Lin and Muhilin Alg, 2009, 57:523 - 534.
  • 8Molnar L. A generalization of Wigner's unitary-antiunitary theorem to Hilbert modules [ J ]. J Math Phys, 1999,40:5544 -5554.
  • 9Zhang X L, Hou J C, He K. Maps preserving numerical radius and cross norms of operator products. Lin. and Multilin. Alg., 2009, 57: 523-534.
  • 10Hou J C, He K, Zhang X L. Maps preserving numerical radius or cross norms of products of self-adjoint operators. Acta. Math. Sinica, to appear.

引证文献2

二级引证文献1

中北大学学报（自然科学版）
2009年 第6期

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