Connectivity of level sets of quadratic forms and Hausdorff-Toeplitz type theorems
type: Item
instance of: scholarly article
title: Connectivity of level sets of quadratic forms and Hausdorff-Toeplitz type theorems
zbMATH Open document ID: 0891.15023
DOI: 10.1023/A:1009760027676
author: A. Markus
author: Yu. I. Lubich
published in: Positivity
publication date: 1998-07-01T00:00:00Z
review text: Given an arbitrary operator \(A: X\to X\) in a complex pre-Hilbert space \(X\), \(\dim X\geq 3\), the authors prove that all level sets \(F(A,\lambda)= \{x\in X:\langle Ax,x\rangle= \lambda\), \(|x|= 1\}\) are connected. Related to this main result, many other ones are derived by specializing \(A\) and \(F(A,\lambda)\).
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15A63
zbMATH DE Number: 1121757
zbMATH Keywords: quadratic forms
zbMATH Keywords: connectivity
zbMATH Keywords: convexity
zbMATH Keywords: generalized numerical range
zbMATH Keywords: Hausdorff-Toeplitz theorem
zbMATH Keywords: pre-Hilbert space
reviewed by: Mihail Voicu
MaRDI profile type: Publication
full work available at URL: a:1009760027676
OpenAlex ID: W141863670
description: scientific article; zbMATH DE number 1121757