Norm of an operator with numerical range in a sector
Chi-Kwong Li, Kuo-Zhong Wang
TL;DR
This paper refines a recent result on the relationship between the norm and numerical radius of operators with numerical range in a sector, providing characterizations of operators that attain the optimal ratio.
Contribution
It offers a refined analysis of the norm-to-numerical radius ratio for operators with numerical range in a sector, including characterizations of extremal operators.
Findings
Characterization of operators attaining the optimal ratio
Properties of extremal operators in the sector
Refinement of Drury's recent result
Abstract
We refine a recent result of Drury concerning the optimal ratio between the norm and numerical radius of a bounded linear operator with numerical range lying in a sector of a circular disk. In particular, characterization is given to the operators attaining the optimal ratio, and properties of such operators are explored.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Heat Transfer and Mathematical Modeling · Advanced Mathematical Modeling in Engineering