二阶算子矩阵代数中的全可导点V 被引量：1

All-derivable point in 2×2 operator matrix algebra V

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摘要研究二阶算子矩阵代数中的全可导点.利用线性映射与算子矩阵代数运算,以及套代数理论的相关结果,给出并证明了第二行第二列元素为可逆算子,其余元素为零算子的二阶矩阵是二阶算子矩阵代数的关于强算子拓扑的全可导点,推广了相关文献中的结果. It is the purpose studying all-derivable point in 2 × 2 operator matrix algebra. Using the operation of linear mapping and matrix algebra, and the related results of nest algebra theory, it is shown in this paper that the matrix （the element of the second row second column is an invertible operator, and the other elements are zero operators） is an all-derivable point of the algebra of all 2 × 2 operator matrices for the strongly operator topology, the result of related articles is generalized,

作者王素芳朱军贾金平

机构地区洛阳理工学院数理部杭州电子科技大学数学研究所天水师范学院数学与统计学院

出处《纯粹数学与应用数学》 CSCD 2010年第5期785-791,共7页 Pure and Applied Mathematics

关键词全可导点二阶算子矩阵可导线性映射套代数 all-derivable point, 2 × 2 operator matrices, derivable linear mapping, nest algebra

分类号 O177.1 [理学—基础数学]

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相关文献

参考文献7

1Zhu Jun,Xiong Changping.Derivable mappings at unit operator on nest algebras[J].Linear Algebra and its Application,2007,422(2-3):721-735.
2王素芳,朱军.二阶算子矩阵代数中的全可导点[J].杭州电子科技大学学报（自然科学版）,2007,27(3):95-98. 被引量：3
3Zhu Jun,Xiong Changping.All-derivable points of operator algebras[J].Linear Algebra and its Application,2007,427(1):1-5.
4Jing Wu,Lu Shijie,Li Pengtong.Characterizations of derivations on some operator algebras[J].Bull Austral Math.Soc.,2002,66(2):227-232.
5Hadwin L B.Local multiplications on algebras spanned by idempotents[J].Linear and Multilinear Algebra,1994,37:259-263.
6Erdos J A.Operator of finite rank in nest algebras[J].J.London Math.Soc.,1968,43:391-397.
7Kenneth R Davidson.Research Notes in Mathematics[M].New York:Longman Scientific and Technical,1988.

二级参考文献5

1[1]Jing Wu,Lu Shijie,Li Pengtong.Characterizations of derivations on some operator algebras[J].Bull Austral Math Soc,2002,66 (2):227-232.
2[2]Zhu Jun,Xiong Changping.Derivable mappings at unit operator on nest algebras[J].Linear Algebra and its Application,2007,422 (2-3):721-735.
3[3]L B Hadwin.Local multiplications on algebras spanned by idempotents[J].Linear and Multilinear Algebra,1994,(37):259-263.
4[4]J A Erdos.Operator of finite rank in nest algebras[J].J London Math Soc,1968,(43):391-397.
5[5]Kenneth R Davidson.Research Notes in Mathematics[M].New York:Longman Scientific &Technical,1988:36.

共引文献2

1王素芳,程志谦,朱军.二阶算子矩阵代数中的全可导点[J].洛阳理工学院学报（自然科学版）,2010,20(3):79-84.
2王素芳,程志谦,朱军.二阶算子矩阵代数中的全可导点Ⅱ[J].数学的实践与认识,2011,41(2):195-200.

同被引文献9

1ZHU Jun, XIONG Chang-ping . All-Derivable Points of Operator Algebras [J]. Linear Algebra and its Application, 2007, 427(1): 1-5.
2ZHU Jun, XIONG Chang-ping, ZHANG Lin. All-Derivable Points in Matrix Algebras [J]. Linear Algebra and its Ap- plications, 2009, 430(8-9)~ 2070-2079.
3ZHAO Sha, ZHU Jun. Jordan All-Derivable Points in the Algebra of All Upper Triangular Matrices [J]. Linear Algebra and its Applications, 2010, 433(11-12): 1922-1938.
4JING Wu, LU Shi-jie, LI Peng-tong. Characterizations of Derivations on Some Operator Algebras [J]. Bull Austral Math Soc, 2002, 66(2): 227-232.
5HADWIN L B. Local Multiplications on Algebras Spanned by Idempotents [J]. Linear and Multilinear Algebra, 1994, 37: 259-263.
6ERDOS J A. Operator of Finite Rank in Nest Algebras [J]. J London Math Soc, 1968, 43: 391-397.
7KENNETH R D. Research Notes in Mathematics [M]. New York: Longman Scientific & Technical, 1988: 36.
8姜超.完备分配格L上的S-幂等矩阵[J].西南师范大学学报（自然科学版）,2010,35(5):23-25. 被引量：1
9王素芳,邵玉丽,朱军.二阶矩阵代数中的全可导点[J].西南大学学报（自然科学版）,2011,33(12):116-120. 被引量：1

引证文献1

1王素芳,张娜.对算子矩阵代数中全可导点的探讨[J].西南师范大学学报（自然科学版）,2013,38(4):40-43.

1王素芳,程志谦,朱军.二阶算子矩阵代数中的全可导点Ⅱ[J].数学的实践与认识,2011,41(2):195-200.
2王素芳,程志谦,朱军.二阶算子矩阵代数中的全可导点[J].洛阳理工学院学报（自然科学版）,2010,20(3):79-84.
3王素芳,贾金平,朱军.二阶算子矩阵代数中的全可导点Ⅲ[J].天水师范学院学报,2011,31(2):4-6.
4王素芳,朱军.二阶算子矩阵代数中的全可导点[J].杭州电子科技大学学报（自然科学版）,2007,27(3):95-98. 被引量：3
5乔丽,黄俊杰,阿拉坦仓.一类二阶算子矩阵的谱性质[J].内蒙古大学学报（自然科学版）,2014,45(5):458-461.
6黄俊杰,阿拉坦仓.一类二阶算子矩阵的谱[J].内蒙古大学学报（自然科学版）,2003,34(3):249-251. 被引量：1
7黄俊杰,阿拉坦仓.一类二阶算子矩阵生成C_0半群的条件[J].内蒙古大学学报（自然科学版）,2007,38(6):605-609.
8王素芳,张娜.对算子矩阵代数中全可导点的探讨[J].西南师范大学学报（自然科学版）,2013,38(4):40-43.
9王红霞.Von Neumann代数上的可导和反可导线性映射[J].咸阳师范学院学报,2007,22(2):11-13. 被引量：3
10于涛.复合算子的自反性[J].辽宁大学学报（自然科学版）,2000,27(2):97-100.

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