上三角算子矩阵的几类固零谱
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摘要
设M_C表示Hilbert空间H_1⊕H_2上的上三角算子矩阵M_C=(ACOB),用∩_*表示∩_(C∈B(H_2,H_1))σ_*(M_C),其中*表示某类谱,称满足等式∩_*=σ_*(M_0)的谱为固零谱,本文集中给出上三角算子矩阵的三类固零谱,并举例说明谱等式σ_*(M_0)=σ_*(A)∪σ_*(B)对这三类固零谱失效.
Let M_C be an upper triangular operator matrix acting on a Hilbert space H_1⊕H_2, where M_C =(ACOB),we denote ∩_(C∈B(H_2,H_1))σ_*(M_C) by ∩_*,where * represents one kind of spectrum. In this paper, we present three kinds of spectrum in an unifying manner, and illustrates in examples that the common equality σ_*(MO) =σ_*(A)∪σ_*(B)is not valid for these spectrums.
Let M_C be an upper triangular operator matrix acting on a Hilbert space H_1⊕H_2, where M_C =(ACOB),we denote ∩_(C∈B(H_2,H_1))σ_*(M_C) by ∩_*,where * represents one kind of spectrum. In this paper, we present three kinds of spectrum in an unifying manner, and illustrates in examples that the common equality σ_*(MO) =σ_*(A)∪σ_*(B)is not valid for these spectrums.
引文
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[2] Conway J B. A course in functional analysis[M]. Springer-Verlag, 1990.
[3] Beauzamy B. Introduction to operator theory and invariant subspaces[M]. Elsevier Science Publishers, Amsterdam, 1988.
[4] Tretter C. Spectra theory of block operator matrices and applications[M]. Imperial College Press, London,2008.
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[7] Hwang I, Lee E 131. The boundedness below of 2 x 2 upper triangular operator matrices[J]. Integr Equ Oper Theory, 2001, 39(3):267-276.
[8] Djordjevic S V, Han Y M. A note on Weyl's theorem for operator matrices[C]//Proc Amer Math Soc, 2002,131(8):2543-2547.
[9] Djordjevic D S. Perturbation of spectra of operator matrices[J]. J Operator Theory, 2002, 48:467-486.
[10] Benhida C, Zerouali E H, Zguitti H. Spectra of upper triangular operator matrices[C]//Proc Amer Math Soc, 2005, 133(10):3013-3020.
[11] Barraa M, Boumazgour M. On the perturbations of spectra of upper triangular operator matrices[J]. J Math Anal Appl, 2008, 347:315-322.
[12] Cao X. Browder spectra for upper triangular operator matrices[J]. J Math Anal Appl, 2008, 342:477-484.
[13]海国军,阿拉坦仓.2x2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.
[14]侯国林,阿拉坦仓.2x2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.
[15] Li Y, Sun X H, Du H K. Intersections of the left and right essential spectra of 2 x 2 upper triangular operator matrices[J]. Bull London Math Soc, 2004, 36(6):811-819.
[16]张澜,阿拉坦仓.一类缺项算子矩阵的谱扰动[J].应用数学学报,2010, 33(1):59-65.
[17]张澜,阿拉坦仓.一类缺项算子矩阵四类点谱的扰动[J].系统科学与数学,2010, 30(5):681-688.
[18] Zhang S, Wu Z, Zhong H. Continuous spectrum, point spectrum and residual spectrum of operator matrices[J]. Linear Algebra Appl, 2010, 433:653-661.
[19]黄俊杰,李春光,阿拉坦仓.2x2上三角算子矩阵的点谱扰动[J].系统科学与数学,2014, 34(2):198-205.
[20] Huang J J, Liu A C, Chen A. Spectra of 2×2 upper triangular operator matrices[J]. Filomat, 2016:3587-3599.
[21]孙炯,王忠.线性算子的谱分析[M].北京:科学出版社,2005.
[2] Conway J B. A course in functional analysis[M]. Springer-Verlag, 1990.
[3] Beauzamy B. Introduction to operator theory and invariant subspaces[M]. Elsevier Science Publishers, Amsterdam, 1988.
[4] Tretter C. Spectra theory of block operator matrices and applications[M]. Imperial College Press, London,2008.
[5] Du H, Pan J. Perturbation of spectrums of 2 x 2 operator matrices[C]//Proc Amer Math Soc, 1994(121):761-766.
[6] Barraa M, Boumazgour M. A note on the spectrum of an upper triangular operator matrices[C]//Proc Amer Math Soc, 2003,(10):3083-3088.
[7] Hwang I, Lee E 131. The boundedness below of 2 x 2 upper triangular operator matrices[J]. Integr Equ Oper Theory, 2001, 39(3):267-276.
[8] Djordjevic S V, Han Y M. A note on Weyl's theorem for operator matrices[C]//Proc Amer Math Soc, 2002,131(8):2543-2547.
[9] Djordjevic D S. Perturbation of spectra of operator matrices[J]. J Operator Theory, 2002, 48:467-486.
[10] Benhida C, Zerouali E H, Zguitti H. Spectra of upper triangular operator matrices[C]//Proc Amer Math Soc, 2005, 133(10):3013-3020.
[11] Barraa M, Boumazgour M. On the perturbations of spectra of upper triangular operator matrices[J]. J Math Anal Appl, 2008, 347:315-322.
[12] Cao X. Browder spectra for upper triangular operator matrices[J]. J Math Anal Appl, 2008, 342:477-484.
[13]海国军,阿拉坦仓.2x2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.
[14]侯国林,阿拉坦仓.2x2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.
[15] Li Y, Sun X H, Du H K. Intersections of the left and right essential spectra of 2 x 2 upper triangular operator matrices[J]. Bull London Math Soc, 2004, 36(6):811-819.
[16]张澜,阿拉坦仓.一类缺项算子矩阵的谱扰动[J].应用数学学报,2010, 33(1):59-65.
[17]张澜,阿拉坦仓.一类缺项算子矩阵四类点谱的扰动[J].系统科学与数学,2010, 30(5):681-688.
[18] Zhang S, Wu Z, Zhong H. Continuous spectrum, point spectrum and residual spectrum of operator matrices[J]. Linear Algebra Appl, 2010, 433:653-661.
[19]黄俊杰,李春光,阿拉坦仓.2x2上三角算子矩阵的点谱扰动[J].系统科学与数学,2014, 34(2):198-205.
[20] Huang J J, Liu A C, Chen A. Spectra of 2×2 upper triangular operator matrices[J]. Filomat, 2016:3587-3599.
[21]孙炯,王忠.线性算子的谱分析[M].北京:科学出版社,2005.