Numerical ranges of Foguel operators

Hwa Long Gau; Kuo Zhong Wang; Pei Yuan Wu

doi:10.1016/j.laa.2020.10.017

Numerical ranges of Foguel operators

Hwa Long Gau, Kuo Zhong Wang, Pei Yuan Wu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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(F_T) is strictly less than 1+(‖T‖/2), (2) if T is a diagonal unitary operator, then 5/2<w(F_T)≤3/2, and (3) if T is a scalar operator aI, then the numerical range W(F_T) is open and is not a circular disc unless a=0.

Original language	English
Pages (from-to)	766-784
Number of pages	19
Journal	Linear Algebra and Its Applications
Volume	610
DOIs	https://doi.org/10.1016/j.laa.2020.10.017
State	Published - 1 Feb 2021

Keywords

Foguel operator
Foguel–Halmos operator
Numerical radius
Numerical range

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10.1016/j.laa.2020.10.017

A Study on Numerical Radii of Tensor Products and Hadamard Products of Matrices
Gau, H.
1/08/20 → 31/07/21
Project: Research

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title = "Numerical ranges of Foguel operators",

abstract = "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 5/2T)≤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.",

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AU - Gau, Hwa Long

AU - Wang, Kuo Zhong

AU - Wu, Pei Yuan

PY - 2021/2/1

Y1 - 2021/2/1

N2 - 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 5/2T)≤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.

AB - 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 5/2T)≤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.

KW - Foguel operator

KW - Foguel–Halmos operator

KW - Numerical radius

KW - Numerical range

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DO - 10.1016/j.laa.2020.10.017

M3 - 期刊論文

AN - SCOPUS:85094119760

SN - 0024-3795

VL - 610

SP - 766

EP - 784

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Numerical ranges of Foguel operators

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Keywords

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A Study on Numerical Radii of Tensor Products and Hadamard Products of Matrices

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