无界2×2分块算子矩阵的本质谱与Weyl谱

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英文篇名：Essential and Weyl Spectra of Unbounded 2×2 Block Operator Matrices 作者：李琳 ; 杨树生 ; 张晓军 ; 阿拉坦仓 英文作者：LI Lin;YANG Shu-sheng;ZHANG Xiao-jun;Alatancang;School of Mathematical Sciences, Inner Mongolia University;Department of Science, Hetao University;Department of Mathematic, Hohhot Minzu College; 关键词：本质谱 ; Weyl谱 ; 分块算子矩阵 英文关键词：essential spectrum;;Weyl spectrum;;block operator matrix 中文刊名：SSJS 英文刊名：Mathematics in Practice and Theory 机构：内蒙古大学数学科学学院;内蒙古河套学院理学系;呼和浩特民族学院数学系; 出版日期：2019-04-08 出版单位：数学的实践与认识 年：2019 期：v.49 基金：国家自然科学基金(11761029);; 内蒙古自治区高等学校科学研究项目(NJZY259),内蒙古自治区高等学校科学研究项目(NJZY17375);; 河套学院科学研究项目自然科学一般类基金(HYZY200702) 语种：中文; 页：SSJS201907028 页数：11 CN：07 ISSN：11-2018/O1 分类号：223-233

摘要

研究无界2×2分块算子矩阵是Fredholm算子、Weyl算子的充要条件;给出了次对角元占优2×2分块算子矩阵的本质谱、Weyl谱与其子块算子本质谱、Weyl谱的关系;研究了主对角元占优2×2分块算子矩阵的本质谱、Weyl谱与其子块算子本质谱、Weyl谱的关系.
        This paper is concerned with the necessary and sufficient conditions that a class of unbounded 2×2 block operator matrices are Fredholm operators or Weyl operators. Some necessary and sufficient conditions are given under which the essential spectrum and the Weyl spectrum of the block operator matrix coincide with the essential spectrum and the Weyl spectrum of its entries.

引文

[1]阿拉坦仓,张鸿庆.一类偏微分方程的Hamilton正则表示[J].力学学报,1999, 31(3):347-357.
    [2]阿拉坦仓,黄俊杰.一类无穷维Hamilton算子纯虚谱的扰动[J].内蒙古大学学报(自然版),2009, 39(1):1-6.
    [3]阿拉坦仓,黄俊杰.无穷维Hamilton算子的谱及相关问题的研究[J].数学进展,2009,38(2):129-145.
    [4]侯国林,阿拉坦仓.一类无穷维Hamilton算子的谱[J].内蒙古大学学报(自然版),2007, 389(3):1247-251.
    [5]侯国林,阿拉坦仓.无穷维Hamilton算子特征的数系的Cauchy主值意义下的完备性[J].中国科学:A-数学,2008, 38(8):904-912.
    [6] Du H K, Pan J. Perturbation of spectrum of 2 x 2 operator matrices[J]. Proc Amer Math Soc, 1994,121(3):761-766.
    [7] Han J K, Lee H Y, Lee W Y. Invertible completions of 2 x 2 upper triangular operator matrices[J].Proc Amer Math Soc, 2000, 129:119-123.
    [8] Zerouali E H, Zguitti H. Perturbation of spectra of operator matricess and local spectral theory[J].J Math Anal Appl, 2006, 324:992-1005.
    [9] Djordjevic S V, Zguitti H. Essential point spectra of operator matrices trough local spectral theory[J]. J Math Anal Appl, 2008, 338:285-291。
    [10] Huang J J, Huang Y, Wang H. Closed range and Fredholm properties of upper-triangular operator matrices[J]. Annals of Functional Analysis, 2015, 6(3):42-52.
    [11] Duggal B P. Browder and Weyl spectra of upper triangular operator matrices[J]. Filomat, 2010,24(2):111-130.
    [12] Kato T. Perturbation of closed operators[M]. Berlin:Springer-Verlag, 1980.
    [13] Tretter C. Spectral theory of block operator matrices and application[M]. Longdon:Imperial College Press, 2008.
    [14] Aienia P. Fredholm and local spectral theorey with applications to multipliers[M]. Dordrecht:Kluwer Academic Publishers, 2004.
    [15] Gohberg I C, Goldberg S, Kaashoek M A. Class of Linear Operators I[M]. Basel:Birkhauser, 1990.
    [16] Qingmei, Huang J J, Alatancang. Essential Weyl and Browder spectra of unbounded upper triagular operator matrices[J]. Linear and Multilinear Algebra, 2015, 1:1-12.