Can a non-Lipschitz function operate non-trivially on a Banach space of functions?
type: Item
instance of: scholarly article
title: Can a non-Lipschitz function operate non-trivially on a Banach space of functions?
zbMATH Open document ID: 0814.47076
author: Alain Bernard
published in: Journal of Functional Analysis
publication date: 1994-08-22T00:00:00Z
review text: Let \(E\) be a subspace of \(C(K)\) (\(K\) a compact set) which separates points and contains the constant functions, and let \(\varphi\) be some real function. The author studies the following problem: Characterize those \(\varphi\) such that the corresponding autonomous Nemytskij operator \(u\mapsto \varphi\circ u\) maps \(E\) into itself. For example, for a non- affine function \(\varphi\) this is possible only for \(E= C(K)\).
reviewed by: Jürgen Appell
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 26A16
zbMATH DE Number: 599809
zbMATH Keywords: autonomous Nemytskij operator
MaRDI profile type: Publication
full work available at URL: jfan.1994.1076
OpenAlex ID: W2019901856
DOI: 10.1006/JFAN.1994.1076
description: scientific article; zbMATH DE number 599809