Symmetry of the spatial numerical ranges of algebra polynomials and of matrix polynomials
type: Item
instance of: scholarly article
title: Symmetry of the spatial numerical ranges of algebra polynomials and of matrix polynomials
zbMATH Open document ID: 0951.47006
DOI: 10.1007/BF02172665
author: Thanassis Chryssakis
published in: Journal of Mathematical Sciences (New York)
publication date: 2000-03-06T00:00:00Z
review text: Let \(E\) be a unital \(*\)-algebra and \(\varphi: E\to{\mathcal L}(H_\varphi)\) a \(*\)-representation. For a polynomial \(P\) with coefficients in \(E\) the \(\varphi\)-spatial numerical range is defined as the set of those complex numbers \(\lambda_0\) such that \((\varphi(P(\lambda_0)) \xi|\xi)= 0\) for some \(\xi\in H_\varphi\) with \((\xi|\xi)= 1\). In this setting and for unital \(lmc\) \(*\)-algebras, where the Bonsall numerical range is considered, conditions are given to imply the numerical range or the union of two numerical ranges being symmetric to the real axis or to a line through the origin.
reviewed by: Gerhard Garske
Mathematics Subject Classification ID: 47A12
Mathematics Subject Classification ID: 46K05
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 1408543
zbMATH Keywords: spatial numerical ranges
zbMATH Keywords: \(*\)-algebra
zbMATH Keywords: \(*\)-representation
zbMATH Keywords: polynomial
zbMATH Keywords: Bonsall numerical range
MaRDI profile type: Publication
cites work: On locally m-convex x-algebras
cites work: Q4863070
cites work: Q3799170
cites work: Q3730448
cites work: Geometrical properties of numerical range of matrix polynomials
full work available at URL: https://doi.org/10.1007/bf02172665
OpenAlex ID: W2093887111
description: scientific article; zbMATH DE number 1408543