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二阶矩阵代数上保Jordan半乘积数值半径或交叉范数的映射

Maps Preserving Numerical Radius or Cross Norms of Jordan semi-Products of Matries on 2×2 Matrix Algebras
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摘要 给出二阶矩阵代数上保单位保Jordan半乘积数值半径的满映射的刻画以及保单位保Jordan半乘积交叉范数的满映射的刻画,补充完善了三阶以上矩阵代数的相应结果. The unital surjective maps on 2 ×2 matrix algebra which preserving the numerical radius of Jordan semi-product of matrices or preserving a cross norm of Jordan semi-products of matrices are characterized. These supplement the corresponding results for maps on β（H） with dim H≥ 3.
作者 钱祖欣 侯晋川
机构地区 太原理工大学理学院数学系
出处 《数学研究》 CSCD 2010年第2期151-161,共11页 Journal of Mathematical Study
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 Jordan半乘积 数值半径 交叉范数 numerical radius cross norms Jordan semi-product
分类号 O151.21 [理学—基础数学]
  • 相关文献

参考文献9

  • 1Zhang 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.
  • 2Hou 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.
  • 3Hou J C, He K, Zhang X L. Nonlinear maps preserving numerical radius of indefinite skew product of operators. Lin. Alg. Appl., 2009, 430: 2240-2253.
  • 4Cui J L, Hou J C. Linear maps preserving the closure of numerical range on nest algebras with maximal atomic nest. Int. Equ. Oper. Theo., 2003, 46: 253-266.
  • 5Cui J L, Hou J C. Non-linear numerical radius isometrics on atomic nest algebras and diagonal algebras. Funct. Anal., 2004, 206: 414-448.
  • 6Li C K, Sze N S. Product of Operators and Numerical Range Preserving Maps. Studia Math., 2006, 174: 169-182.
  • 7Hou J C, Di Q H. Maps preserving numerical range of operator products. Proc. Amer. Math. Soe., 2006, 134: 1435-1446.
  • 8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
  • 9Molnar L. A generalization of Wigner's unitary-antiunitary theorem to Hilbert modules. J. Math. Phys., 1999, 40: 5544-5554.

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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数学研究
2010年 第2期

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