Numerical ranges of Foguel operators

被引：4
作者：
Gau, Hwa-Long [1 ]
Wang, Kuo-Zhong [2 ]
Wu, Pei Yuan [2 ]
机构：
[1] Natl Cent Univ, Dept Math, Chungli 32001, Taiwan
[2] Natl Chiao Tung Univ, Dept Appl Math, Hsinchu 30010, Taiwan
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2021年 / 610卷
关键词：
Numerical range; Numerical radius; Foguel operator; Foguel-Halmos operator;
D O I：
10.1016/j.laa.2020.10.017
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study properties of the numerical ranges of Foguel operators F-T = [S* T 0 S], where Sis the simple unilateral shift and Tis some operator, both acting on l(2). Among other things, we show that (1) if Tis nonzero compact, then the numerical radius w(F-T) is strictly less than 1 +(parallel to T parallel to/2), (2) if T is a diagonal unitary operator, then root 5/2 < w(F-T) <= 3/2, and (3) if Tis a scalar operator aI, then the numerical range W(F-T) is open and is not a circular disc unless a = 0. (C) 2020 Elsevier Inc. All rights reserved.
引用
收藏
页码：766 / 784
页数：19
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