The Conditions of Quadratic Numerical Range of Block Operator Matriz Equal to Its Spectrum

摘要：

Let Γ be a bounded linear operator acting on H = H1 ⊕ H2 with block operator matrix r =(A B C D),W2(Γ) and σ(Γ) denote the quadratic numerical range and the spectrum of Γ, respectively. We show that ifdim H >2 and F is a compact operator, then W2(Γ) =σ(Γ) if and only if there exist λ,μ∈C such that A= λI, D=μl and B=0 or C =0, and also give an example to show that there exists a bounded operator Γ satisfying W2(Γ)=σ(Γ), but A≠λI and D≠μl for all λ,μ∈C.

关键词： block operator matriz quadratic numerical range spectrum

作者: Ping Liu Lihong Sun

作者单位: School of Information Science and Technology,Qingdao University of Science and Technology, Qingdao, Department of Mathematics, Qingdao University of Science and Technology, Qingdao, 266061, China

会议类型: 国际会议

会议名称: The Third International Workshop on Applied Matriz Theory(第三届国际矩阵分析与应用会议)

会议地点: 杭州

会议语种:英文

页码: 780-783

在线出版日期: 2009-07-09（万方平台首次上网日期，不代表论文的发表时间）