2×2上三角无界算子矩阵的谱  

Spectra of 2 × 2 upper triangular operator matrices with unbounded entries

作　　者：阿拉坦仓[1,2] 青梅[1] 吴德玉[1] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]内蒙古民族学院数学系,呼和浩特010051

出　　处：《中国科学：数学》2016年第2期157-168,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11371185;11101200和11362011);内蒙古自然科学基金(批准号:2013ZD01和2013MS0103)资助项目

摘　　要：本文研究了Hilbert空间中的对角定义的2×2上三角闭线性算子矩阵的谱、近似点谱、亏谱和本质谱的性质,进而得到了算子矩阵的谱、近似点谱和亏谱分别等于对角算子的谱、近似点谱和亏谱的并集的充要条件;还得到了算子矩阵的本质谱等于对角算子的本质谱的并集的充分条件.作为应用,本文还得到了对角定义的上三角无穷维Hamilton算子的谱性质.In this paper, some properties of the spectrum, the approximate point spectrum, the detect spectrum and the essential spectrum of unbounded 2×2 upper triangular operator matrices with diagonal domain in Hilbert space are studied. Moreover, a necessary and sufficient condition under which the spectrum （resp. the approximate point spectrum, the detect spectrum） of operator matrices is equal to the union of the spectrum （resp. the approximate point spectrum, the detect spectrum） of diagonal entries is given. We also obtain a sufficient condition under which the essential spectrum of operator matrices is equal to the union of the essential spectrum of diagonal entries. In the end, the theory is applied to Hamiltonian operator matrix arising in mathematical physics.

关 键 词：上三角闭算子矩阵 近似点谱 亏谱 本质谱 无穷维HAMILTON算子 

分 类 号：O177.1[理学—数学]