A numerical range for nonlinear operators in smooth Banach spaces
type: Item
instance of: scholarly article
title: A numerical range for nonlinear operators in smooth Banach spaces
zbMATH Open document ID: 0849.47036
DOI: 10.4171/ZAA/709
author: M. Dörfner
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1996-06-13T00:00:00Z
review text: The author defines and discusses a numerical range for nonlinear operators in smooth Banach spaces, and studies its relations with certain spectral sets. He shows, in particular, that the spectrum of a Lipschitz operator in the sense of \textit{R. I. Kachurovskij} [Dokl. Akad. Nauk SSSR 188, 274-277 (1969; Zbl 0197.40402)] is contained in the smallest Jordan domain containing the numerical range.
Mathematics Subject Classification ID: 47J10
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47A12
zbMATH DE Number: 889006
zbMATH Keywords: numerical range for nonlinear operators
zbMATH Keywords: smooth Banach spaces
zbMATH Keywords: spectral sets
zbMATH Keywords: Lipschitz operator
zbMATH Keywords: Jordan domain
reviewed by: Jürgen Appell
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/zaa/709
OpenAlex ID: W2025473022
description: scientific article; zbMATH DE number 889006