# Numerical ranges of Foguel operators

Hwa Long Gau, Kuo Zhong Wang, Pei Yuan Wu

## 摘要

We study properties of the numerical ranges of Foguel operators [Formula presetend], where S is the simple unilateral shift and T is some operator, both acting on ℓ2. Among other things, we show that (1) if T is nonzero compact, then the numerical radius w(FT) is strictly less than 1+(‖T‖/2), (2) if T is a diagonal unitary operator, then 5/2<w(FT)≤3/2, and (3) if T is a scalar operator aI, then the numerical range W(FT) is open and is not a circular disc unless a=0.

原文 ???core.languages.en_GB??? 766-784 19 Linear Algebra and Its Applications 610 https://doi.org/10.1016/j.laa.2020.10.017 已出版 - 1 2月 2021

## 指紋

• ### 矩陣張量積與哈達瑪積的數值半徑之研究

Gau, H.

1/08/2031/07/21

研究計畫: Research