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.

引用

页码：487 / 499

页数：13

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