上三角算子矩阵的(αβ)-本质谱

海国君, 阿拉坦仓

数学学报 ›› 2014, Vol. 57 ›› Issue (3) : 569-580.

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PDF(442 KB)
数学学报 ›› 2014, Vol. 57 ›› Issue (3) : 569-580. DOI: 10.12386/A2014sxxb0053
论文

上三角算子矩阵的(αβ)-本质谱

    海国君, 阿拉坦仓
作者信息 +

On the (α,β)-Essential Spectrum of Upper Triangular Operator Matrices

    Guo Jun HAI, Alatancang
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文章历史 +

摘要

HK为可分的无穷维Hilbert空间. 对于给定的算子ABH)和B∈B(K),本文给出存在(和所有) CBK, H),使得(???569-01.jpg???)为(αβ)-半Fredholm算子的充分必要条件. 此外, 得到了相关结论.

Abstract

Let H and K be separable infinite dimensional Hilbert spaces, and let AB(H) and BB(K), be given operators. A necessary and sufficient condition is obtained for (???569-01.jpg???) to be an (α,β)- semi-Fredholm operator for some (respectively, all) CB(K, H).Furthermore, some related results are obtained.

关键词

本质谱 / 算子矩阵 / Fredholm算子

Key words

essential spectra / operator matrices / Fredholm operator

引用本文

导出引用
海国君, 阿拉坦仓. 上三角算子矩阵的(αβ)-本质谱. 数学学报, 2014, 57(3): 569-580 https://doi.org/10.12386/A2014sxxb0053
Guo Jun HAI, Alatancang. On the (α,β)-Essential Spectrum of Upper Triangular Operator Matrices. Acta Mathematica Sinica, Chinese Series, 2014, 57(3): 569-580 https://doi.org/10.12386/A2014sxxb0053

参考文献

[1] Barraa M., Boumazgour M., On the perturbations of spectra of upper triangular operator matrices, J. Math. Anal. Appl., 2008, 347: 315-322.
[2] Cao X., Limits of hypercyclic and supercyclic operator matrices, J. Aust. Math. Soc., 2008, 85: 367-376.
[3] Cao X., Guo M., Meng B., Semi-Fredholm spectrum and Weyl’s theorem for operator matrices, Acta Mathematica Sinica, English Series, 2006, 22(1): 169-178.
[4] Cao X., Meng B., Essential approximate point spectra and Weyl’s theorem for operator matrices, J. Math. Anal. Appl., 2005, 304: 759-771.
[5] Conway J. B., A Course in Functional Analysis, Springer-Verlag, New York, 1985.
[6] Djordjević D. S., Perturbations of spectra of operator matrices, J. Operator Theory, 2002, 48: 467-486.
[7] Djordjević D. S., Kolundžija M. Z., Generalized invertibility of operator matrices, Ark. Mat., 2012, 50: 259-267.
[8] Douglas R. G., Banach Algebra Technique in Operator Theory, 2nd Edition, Springer Verlag, New York, 1998.
[9] Du H., Pan J., Perturbation of spectrums of 2×2 operator matrices, Proc. Amer. Math. Soc., 1994, 121: 761-766.
[10] Gurvits L., Rodman L., Spitkovsky I., Spectral assignment for Hilbert space operators, Houston J. Math., 1991, 17: 501-523.
[11] Hwang I. S., Lee W. Y., The boundedness below of 2×2 upper triangular operator matrices, Integral Equations Operator Theory, 2001, 39: 267-276.
[12] Müller V., Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras, 2nd Edition, Birkhäuser-Verlag, Basel, 2007.

基金

国家自然科学基金(10962004);内蒙古自然科学基金(2011MS0104);内蒙古自治区高等院校科学技术研究重点项目(NJZZ11011);内蒙古大学高层次引进人才科研启动项目(Z20100116)
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