Numerical range of the Foguel–Halmos operator

Hwa Long Gau; Kuo Zhong Wang; Pei Yuan Wu

doi:10.4064/sm201020-30-7

Numerical range of the Foguel–Halmos operator

Hwa Long Gau, Kuo Zhong Wang, Pei Yuan Wu

Department of Mathematics

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

1 Scopus citations

Abstract

We study properties of the numerical range of the Foguel–Halmos operator FT = ^{[ S}₀^{∗ T}_S^] on ℓ² ⊕ ℓ², where S is the simple unilateral shift and T = diag(a1, a2, . . .) with an = 1 if n = 3^k for some k ≥ 1 and an = 0 otherwise. Among other things, we show that the numerical range W(FT ) is neither open nor closed, and give lower and upper bounds for the numerical radius w(FT ).

Original language	English
Pages (from-to)	267-292
Number of pages	26
Journal	Studia Mathematica
Volume	263
Issue number	3
DOIs	https://doi.org/10.4064/sm201020-30-7
State	Published - 2022

Keywords

Foguel operator
Foguel–Halmos operator
numerical radius
numerical range

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abstract = "We study properties of the numerical range of the Foguel–Halmos operator FT = [ S0∗ TS] on ℓ2 ⊕ ℓ2, where S is the simple unilateral shift and T = diag(a1, a2, . . .) with an = 1 if n = 3k for some k ≥ 1 and an = 0 otherwise. Among other things, we show that the numerical range W(FT ) is neither open nor closed, and give lower and upper bounds for the numerical radius w(FT ).",

keywords = "Foguel operator, Foguel–Halmos operator, numerical radius, numerical range",

author = "Gau, {Hwa Long} and Wang, {Kuo Zhong} and Wu, {Pei Yuan}",

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T1 - Numerical range of the Foguel–Halmos operator

AU - Gau, Hwa Long

AU - Wang, Kuo Zhong

AU - Wu, Pei Yuan

N1 - Publisher Copyright: © Instytut Matematyczny PAN, 2022.

PY - 2022

Y1 - 2022

N2 - We study properties of the numerical range of the Foguel–Halmos operator FT = [ S0∗ TS] on ℓ2 ⊕ ℓ2, where S is the simple unilateral shift and T = diag(a1, a2, . . .) with an = 1 if n = 3k for some k ≥ 1 and an = 0 otherwise. Among other things, we show that the numerical range W(FT ) is neither open nor closed, and give lower and upper bounds for the numerical radius w(FT ).

AB - We study properties of the numerical range of the Foguel–Halmos operator FT = [ S0∗ TS] on ℓ2 ⊕ ℓ2, where S is the simple unilateral shift and T = diag(a1, a2, . . .) with an = 1 if n = 3k for some k ≥ 1 and an = 0 otherwise. Among other things, we show that the numerical range W(FT ) is neither open nor closed, and give lower and upper bounds for the numerical radius w(FT ).

KW - Foguel operator

KW - Foguel–Halmos operator

KW - numerical radius

KW - numerical range

UR - http://www.scopus.com/inward/record.url?scp=85149696366&partnerID=8YFLogxK

U2 - 10.4064/sm201020-30-7

DO - 10.4064/sm201020-30-7

M3 - 期刊論文

AN - SCOPUS:85149696366

SN - 0039-3223

VL - 263

SP - 267

EP - 292

JO - Studia Mathematica

JF - Studia Mathematica

IS - 3

ER -

Numerical range of the Foguel–Halmos operator

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Keywords

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