The spectrum of the product of operators, and the product of their numerical ranges

被引：6
作者：
Li, Chi-Kwong [1 ]
Tsai, Ming-Cheng [2 ]
Wang, Kuo-Zhong [3 ]
Wong, Ngai-Ching [2 ]
机构：
[1] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA
[2] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan
[3] Natl Chiao Tung Univ, Dept Appl Math, Hsinchu 30010, Taiwan
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2015年 / 469卷
关键词：
Numerical range; Spectrum; Positive operators; MATRICES;
D O I：
10.1016/j.laa.2014.11.024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that a compact operator A is a multiple of a positive semi-definite operator if and only if sigma(AB) subset of <(W(A)W(B))over bar>, for all (rank one) operators B. An example of a normal operator is given to show that the equivalence conditions may fail in general. We then obtain conditions to identify other classes of operators A so that equivalence conditions hold. (C) 2014 Elsevier Inc. All rights reserved.
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页码：487 / 499
页数：13
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