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

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

4 引文斯高帕斯（Scopus）

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(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.

原文	???core.languages.en_GB???
頁（從 - 到）	766-784
頁數	19
期刊	Linear Algebra and Its Applications
卷	610
DOIs	https://doi.org/10.1016/j.laa.2020.10.017
出版狀態	已出版 - 1 2月 2021

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10.1016/j.laa.2020.10.017

矩陣張量積與哈達瑪積的數值半徑之研究
Gau, H.-L. (PI)
1/08/20 → 31/07/21
研究計畫: Research

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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 - Wang, Kuo Zhong

AU - Wu, Pei Yuan

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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

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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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矩陣張量積與哈達瑪積的數值半徑之研究

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