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二阶自伴矩阵空间上保数值半径或交叉范数的映射 被引量：1

Maps Preserving Numerical Radius or Cross Norms of Products of Self-adjoint Matrics on 2×2 Matrix Space
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摘要 本文给出由所有二阶自伴矩阵组成的实空间上保矩阵数值半径的满映射的刻画以及保矩阵交叉范数的满映射的刻画,补充完善了三阶以上自伴矩阵组成的实空间上的相应结果. The unital surjective maps on 2×2 self-adjoint matix space which preserving the numerical radius of product or Jordan semi-product of self-adjoint matrices or preserving a cross norm of products or Jordan semi-products of self-adjoint matrices are characterized.These supplement the corresponding results for n×n self-adjoint matrix space with n≥3.
作者 钱祖欣 张秀玲
机构地区 太原理工大学数学系 山西师范大学数学与计算机科学学院
出处 《山西师范大学学报（自然科学版）》 2010年第1期1-8,共8页 Journal of Shanxi Normal University(Natural Science Edition)
基金 国家自然科学基金资助项目(1077157) 山西省自然科学基金资助项目(2007011016)
关键词 矩阵乘积 数值半径 交叉范数 numerical radius cross norms space of self-adjoint operators product of operators
分类号 O177.1 [理学—基础数学]
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参考文献9

  • 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.
  • 9张文芳,侯晋川.二阶矩阵代数上保乘积数值半径或交叉范数的映射[J].中北大学学报（自然科学版）,2009,30(6):506-511. 被引量：2

二级参考文献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.

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山西师范大学学报（自然科学版）
2010年 第1期

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