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PDF(470 KB)
PDF(470 KB)
上三角算子矩阵谱的自伴扰动
Self-Adjoint Perturbation of Spectra of Upper Triangular Operator Matrices
本文研究了自伴算子的构造方法, 基此得到一类上三角算子矩阵谱的自伴扰动. 结果表明对于此类算子, 其谱的自伴扰动包含通常的谱扰动, 并举例说明后者可以是前者的真子集. 作为应用, 将上述结果推广到无穷维Hamilton算子情形.
In this paper, we first investigate method of constructing self-adjoint operators. Then, based on the method, the self-adjoint perturbation of spectra of a class of upper triangular operator matrices is obtained. It can be seen that the self-adjoint perturbation of spectra contains the general perturbation of spectra. Moreover, an interesting example shows that this kind of inclusion may be proper. As an application, these results are developed to infinite dimensional Hamiltonian operators.
谱的自伴扰动 / 2×2算子矩阵 / 无穷维Hamilton算子 {{custom_keyword}} /
self-adjoint perturbation of spectrum / 2 × / 2 operator matrix / infinite dimensional Hamiltonian operator {{custom_keyword}} /
[1] Han J. K., Lee H. Y., Lee W. Y., Invertible completions of 2×2 upper triangular operator matrices, Proc. Amer. Math. Soc., 2000, 129(1): 119--123.
[2] Hwang I. S., Lee W. Y., The boundedness below of 2×2 upper triangular operator matrices, Integr. Equat. Oper. Th., 2001, 39: 267--276.
[3] Du H. K., Pan J., Perturbation of spectrums of 2×2 operator matrices, Proc. Amer. Math. Soc., 121(3): 761--776.
[4] Barraa M., Boumazgour M., A note on the spectrum of an upper triangular operator matrices, Proc. Amer. Math. Soc., 2003, 131(10): 3083--3088.
[5] Benhida C., Zerouali E. H., Guitti H., Spectrum of upper triangular operator matrices, Proc. Amer. Math. Soc., 2005, 133(10): 3013--3020.
[6] Djordjevi'c D. S., Perturbation of spectrums of operator matrices, J. Operat. Theor., 2002, 48: 467--486.
[7] Li Y., Sun X. H., Du H. K., Intersections of the left and right essential spectra of 2×2 upper triangular operator matrices, Bull. London Math. Soc., 2004, 36(6): 811--819.
[8] Li Y., Du H. K., The intersection of essential approximate point spectra, J. Math. Anal Appl., 2006, 323: 1171--1183.
[9] Cao X. H., Browder spectra for upper triangular operator matrices. J. Math. Anal Appl., In Press.
[10] Hou G. L., Alatancang, Perturbation of spectrums of 2×2 upper triangular operator matrices, J. Sys. Sci. & Math. Scis., 2006, 26(3): 257--263 (in Chinese).
[11] Zhong W. X., A New Systematic Method in Elasticity Theory, Dalian: Dalian University of Technology Press, 1995 (in Chinese).
[12] Azizov T. Ya., Dijksma A., Gridneva I. V., On the boundedness of Hamiltonian operators, Proc. Amer. Math. Soc., 2002, 131(2): 563--576.
[13] Kurina G. A., Invertibility of nonnegatively Hamiltonian operators in a Hilbert space, Differ. Equ., 2001, 37(6): 880--882.
[14] Huang J. J., Alatancang, Fan X. Y., Structure of the spectrum of infinite dimensional Hamiltonian operators, Sci. China Ser. A, Math., 2008, 38(1): 71--78 (in Chinese).
[15] Huang J. J., Alatancang, The pure imaginary spectrum of triangular infinite dimensional Hamiltonian operators, J. Spectral Math. Appl., 2006, 1: 48--58.
[16] Hou G. L., Alatancang, Huang J. J., Invertibility of an operator appearing in the linear-quadratic optimal control problems in a Hilbert space, Acta Mathemtica Sinica, Chinese Series, 2007, 50(2): 473--480.
[17] Alatancang, Huang J. J., A theorem on C0 semigroups generated by a class of infinite dimensional Hamiltonian operators, Appl. Math. J. Chinese Univ., Ser. A, 2006, 21(3): 357--364 (in Chinese).
[18] Li Y., The Perturbations on the Spectra of Operator Matrix, Master degree Dissertation, Xi'an: Department of Mathematics, Shanxi Normal University, 2004 (in Chinese).
[19] Gohberg I., Goldberg S., Kaashoek M. A., Classes of Linear Operators, Vol.1. Basel: Birkhäuser-Verlag, 1990.
[20] Taylor A. E., Lay D. C., Introduction to Functional Analysis, 2nd ed. New York: John Wiley & Sons, 1980.
国家自然科学基金(10962004, 11061019);高等学校博士学科点专项基金(20070126002);教育部春晖计划(Z2009-1-01010);教育部留学回国人员科研启动基金;内蒙古自治区自然科学基金(2009BS0101)
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