上三角算子矩阵的谱性质
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摘要
利用空间分解方法研究了上三角算子矩阵的Moore-Penrose谱、剩余谱、连续谱、Weyl谱、Browder谱和Drazin谱,得到它们分别包含于对角元的相应谱的并集的充分必要条件.
Based on the space decomposition technique,some sufficient and necessary conditions are given for the Moore-Penrose spectrum,residual spectrum,continuous spectrum,Weyl spectrum,Browder spectrum and Drazin spectrum of upper triangular operator matrices contained in the union of the corresponding spectra of their diagonal entries.
Based on the space decomposition technique,some sufficient and necessary conditions are given for the Moore-Penrose spectrum,residual spectrum,continuous spectrum,Weyl spectrum,Browder spectrum and Drazin spectrum of upper triangular operator matrices contained in the union of the corresponding spectra of their diagonal entries.
引文
[1]Djordjevi′cD S.Perturbations of spectra of operator matrices[J].J.Operator Theory,2002,48(3):467-486.
[2]侯国林,阿拉坦仓.2×2阶上三角算子矩阵的谱扰动[J].系统科学与数学,2006,26(3):257-263.
[3]海国君,阿拉坦仓.2×2阶上三角算子矩阵的Moore-Penrose谱[J].系统科学与数学,2009,29(7):962-970.
[4]Djordjevi′cS V,Han Y M.A note on Weyl’s theorem for operator matrices[J].Proc Amer Math Soc,2002,131(8):2543-2547.
[5]刘爱春,阿拉坦仓,黄俊杰.2×2阶上三角算子矩阵的点剩余谱扰动[J].黑龙江大学学报,2012,29(1):51-55.
[6]Huang Junjie,Liu Aichun,Chen Alatancang.Spectra of 2×2upper triangular operator matrices[J].Filomat,2016,30(13):3587-3599.
[7]刘爱春.2×2上三角算子矩阵的谱[D].呼和浩特:内蒙古大学,2011.
[8]Zhang S,Wu Z,Zhong H.Continuous spectrum,point spectrum and residual spectrum of operator matrices[J].Linear Algebra Appl,2010,433(3):653-661.
[9]Taylor A E,Lay D C.Introduction to Functional Analysis,Second Edition[M].New York:John Wiley&Sons,1980.
[10]Djordjevic D S,Stanimirovic P S.On the generalized Drazin inverse and generalized resolvent[J].Czechoslovak Math J,2001,51(3):617-634.
[2]侯国林,阿拉坦仓.2×2阶上三角算子矩阵的谱扰动[J].系统科学与数学,2006,26(3):257-263.
[3]海国君,阿拉坦仓.2×2阶上三角算子矩阵的Moore-Penrose谱[J].系统科学与数学,2009,29(7):962-970.
[4]Djordjevi′cS V,Han Y M.A note on Weyl’s theorem for operator matrices[J].Proc Amer Math Soc,2002,131(8):2543-2547.
[5]刘爱春,阿拉坦仓,黄俊杰.2×2阶上三角算子矩阵的点剩余谱扰动[J].黑龙江大学学报,2012,29(1):51-55.
[6]Huang Junjie,Liu Aichun,Chen Alatancang.Spectra of 2×2upper triangular operator matrices[J].Filomat,2016,30(13):3587-3599.
[7]刘爱春.2×2上三角算子矩阵的谱[D].呼和浩特:内蒙古大学,2011.
[8]Zhang S,Wu Z,Zhong H.Continuous spectrum,point spectrum and residual spectrum of operator matrices[J].Linear Algebra Appl,2010,433(3):653-661.
[9]Taylor A E,Lay D C.Introduction to Functional Analysis,Second Edition[M].New York:John Wiley&Sons,1980.
[10]Djordjevic D S,Stanimirovic P S.On the generalized Drazin inverse and generalized resolvent[J].Czechoslovak Math J,2001,51(3):617-634.