A new approach to numerical radius of quadratic operators
type: Item
instance of: scholarly article
title: A new approach to numerical radius of quadratic operators
zbMATH Open document ID: 1498.47020
author: Jamal Rooin
author: Saeed Karami
author: Masoomeh Ghaderi Aghideh
published in: Annals of Functional Analysis
publication date: 2020-07-17T00:00:00Z
review text: The authors give an elementary approach for computation of the numerical radius and norms of the real and imaginary parts of quadratic operators. Generally, this method is based on proving the maximum of a desired function is equal to one of its suitable upper bounds, via successively establishing equality of this maximum with some of its intermediate upper bounds. This method is illustrated in Theorem~2, Lemma~2 and Proposition~1 and it appears that it can be used in other similar situations. Section~2 is focused on reviewing some classical known results on the numerical radius and norms of the real and imaginary parts of quadratic operators. In [Linear Multilinear Algebra 37, No. 1--3, 13--24 (1994; Zbl 0814.15017)] \textit{C. R. Johnson} et al.\ computed the numerical radius of 2-by-2 matrices from the boundary of their numerical ranges. In Section 3, using a new method, the authors obtain the numerical radius of a quadratic operator in some important special cases. Finally in Section 4, utilizing again this method, the authors obtain the norms of the real and imaginary parts of a quadratic operator in terms of its norm.
reviewed by: V. Lokesha
Mathematics Subject Classification ID: 47A12
zbMATH DE Number: 7222432
zbMATH Keywords: numerical radius
zbMATH Keywords: quadratic operator
zbMATH Keywords: 2-nilpotent operator
zbMATH Keywords: involution operator
zbMATH Keywords: idempotent operator
MaRDI profile type: Publication
full work available at URL: s43034-020-00072-y
OpenAlex ID: W3022734590
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DOI: 10.1007/S43034-020-00072-Y
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description: scientific article; zbMATH DE number 7222432