Possible Spectrums of 3×3 Upper Triangular Operator Matrices  

3×3阶上三角型算子矩阵的可能谱(英文)

作　　者：海国君 阿拉坦仓 

机构地区：[1]Department of Mathematics,Inner Mongolia University

出　　处：《Journal of Mathematical Research and Exposition》2009年第4期649-661,共13页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China (No.10562002);the Specialized Research Foundation for the Doctoral Program of Higher Education (No.20070126002);the Scientific Research Foun-dation for the Returned Overseas Chinese Scholars

摘　　要：Let H1, H2 and H3 be infinite dimensional separable complex Hilbert spaces. We denote by M（D,V,F） a 3×3 upper triangular operator matrix acting on Hi ＋H2＋ H3 of theform M（D,E,F）=（A D F 0 B F 0 0 C）.For given A ∈ B（H1）, B ∈ B（H2） and C ∈ B（H3）, the sets ∪D,E,F^σp（M（D,E,F））,∪D,E,F ^σr（M（D,E,F））,∪D,E,F ^σc（M（D,E,F）） and ∪D,E,F σ（M（D,E,F）） are characterized, where D ∈ B（H2,H1）, E ∈B（H3, H1）, F ∈ B（H3,H2） and σ（·）, σp（·）, σr（·）, σc（·） denote the spectrum, the point spectrum, the residual spectrum and the continuous spectrum, respectively.Let H1,H2 and H3 be infinite dimensional separable complex Hilbert spaces.We denote by M(D,E,F) a 3×3 upper triangular operator matrix acting on H1⊕ H2⊕ H3 of the form M(D,E,F)=.For given A∈B(H1),B∈B(H2) and C∈B(H3),the sets ∪D,E,F σp(M(D,E,F)),∪D,E,F σr(M(D,E,F)),∪D,E,F σc(M(D,E,F)) and ∪D,E,F σ(M(D,E,F)) are characterized,where D∈B(H2,H1),E∈B(H3,H1),F∈B(H3,H2) and σ(·),σp(·),σr(·),σc(·) denote the spectrum,the point spectrum,the residual spectrum and the continuous spectrum,respectively.

关 键 词：3×3 upper triangular operator matrices point spectrum continuous spectrum residual spectrum spectrum. 

分 类 号：O177.1[理学—数学] G633.6[理学—基础数学]