2×2有界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 2 × 2 Bounded Block Operator Matrices 作者：李琳 ; 阿拉坦仓 英文作者：Li Lin;Alatancang;School of Mathematical Sciences, Inner Mongolia University;Department of Mathematics and Computer, Hetao College;Department of Mathematics, Hohhot Minzu College; 关键词：本质谱 ; Weyl谱 ; 块算子矩阵 英文关键词：Essential spectrum;;Weyl spectrum;;Block operator matrices 中文刊名：SXWX 英文刊名：Acta Mathematica Scientia 机构：内蒙古大学数学科学学院;河套学院数学与计算机系;呼和浩特民族学院数学系; 出版日期：2019-06-15 出版单位：数学物理学报 年：2019 期：v.39 基金：国家自然科学基金(11761029,11861048);; 内蒙古自然科学基金(2016MS0105);; 河套学院自然科学基金(HYZY201702)~~ 语种：中文; 页：SXWX201903003 页数：10 CN：03 ISSN：42-1226/O 分类号：17-26

摘要

研究了2×2有界块算子矩阵是Fredholm算子、Weyl算子的充要条件;给出了2×2有界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 bounded 2 x 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,钟万勰.一类偏微分方程的Hamilton正则表示·力学学报,1999,31(3):347-357Alatancang,Zhang H Q,Zhong W X.The canonical Hamiltonian representations in a class of partial differential equation.Acta Mechanica Sinica,1999,31(3):347-357
    [2]阿拉坦仓,海国君.一类无穷维Hamilton算子的本质谱及其应用.数学物理学报,2013,33A(5):984-992Alatancang,Hai G J.The essential spectrum for a class of infinite dimensional Hamiltonian operator and its applications.Acta Math Sci,2013,33A(5):984-992
    [3]王华,阿拉坦仓,黄俊杰.无穷维Hamilton算子特征值的代数指标.数学物理学报,2011,31A(5):1266-1272Wang H,Alatancang,Huang J J.Algebraic index of eigenvalues of infinite dimensional Hamiltonian operators.Acta Math Sci,2011,31A(5):1266-1272
    [4]侯国林,阿拉坦仓.一类无穷维Hamilton算子的谱.内蒙古大学学报(自然科学版),2007,38(3):247-251Hou G L,Alatancang.On the spectra for a class of infinite Hamiltonian operators.Journal of Inner Mongolia University(Natural Science Edition),2007,38(3):247-251
    [5]吴德玉,阿拉坦仓.无穷维Hamilton算子特征函数系的Cauchy主值意义下的完备性.中国科学A辑(数学),2008,38(8):904-912Wu D Y,Alatancang.Completeness in the sense of Cauchy proncipal value of the eigenfunction systems of infinite dimensional Hamiltonian operator.Science in China Series A-Mathematics,2008,38(8):904-912
    [6]Du H K,Pan J.Perturbation of spectrum of 2 x 2 operator matrices.Proc Amer Math Soc,1994,121(3):761-766
    [7]Han J K,Lee HY,Lee W Y.Invertible completions of 2 x 2 upper triangular operator matrices.Proc Amer Math Soc,2000,128:119-123
    [8l]Zerouali E H,Zguitti H.Perturbation of spectra of operator matricess and local spectral theory.J Math Anal Appl,2006,324:992-1005
    [9l]Djordjevic S V,Zguitti H.Essential point spectra of operator matrices trough local spectral theory.J Math Anal Appl,2008,338:285-291
    [10]Bai Q M,Huang J J,Chen A.Weyl type theorems of 2 x 2 upper triangular operator matrices.J Math Anal Appl,2016,434:1065-1076
    [11]Aienia P.Fredholm and Local Spectral Theory with Applications to Multipliers.Dordrecht:Kluwer Academic Publishers,2004
    [12]Huang J J,Huang Y,Wang H.Closed range and Fredholm properties of upper-triangular operator matrices.Annals of Functional Analysis,2015,6(3):42-52
    [13]Duggal B P.Browder and Weyl spectra of upper triangular operator matrices.Filomat,2010,24(2):111-130
    [14]Gohberg I C,Goldberg S,Kaashoek M A.Class of Linear Operators I.Basel:Birkh(a|¨)user,1990