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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 ℓ^{2}. 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 (fromto)  766784 
Number of pages  19 
Journal  Linear Algebra and Its Applications 
Volume  610 
DOIs  
State  Published  1 Feb 2021 
Keywords
 Foguel operator
 Foguel–Halmos operator
 Numerical radius
 Numerical range
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Dive into the research topics of 'Numerical ranges of Foguel operators'. Together they form a unique fingerprint.Projects
 1 Finished

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