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

页码：766 / 784

页数：19

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