On the range of the derivative of Gâteaux-smooth functions on separable Banach spaces
type: Item
instance of: scholarly article
title: On the range of the derivative of Gâteaux-smooth functions on separable Banach spaces
zbMATH Open document ID: 1073.46035
DOI: 10.1007/BF02786693
author: Robert Deville
author: Petr Hájek
published in: Israel Journal of Mathematics
publication date: 2005-05-03T00:00:00Z
review text: The authors study the range of the derivative of a Gâteaux-differentiable function \(f\) between Banach spaces with a particular emphasis on the phenomena that may happen when \(f\) is Gâteaux-differentiable but fails to be Fréchet-differentiable. The authors prove that there is a Gâteaux-differentiable Lipschitz function from \(l_1\) to \(\mathbb R^2\) whose derivative ``jumps'' everywhere.
Mathematics Subject Classification ID: 46G05
zbMATH DE Number: 2164543
zbMATH Keywords: Lipschitz function
zbMATH Keywords: Gâteaux differentiability
reviewed by: S. S. Kutateladze
MaRDI profile type: Publication
cites work: James' theorem fails for starlike bodies
cites work: On the range of the derivatives of a smooth function between Banach spaces
cites work: Exact Filling of Figures with the Derivatives of Smooth Mappings Between Banach Spaces
cites work: The range of the gradient of a continuously differentiable bump
cites work: The range of the gradient of a Lipschitz \(C^1\)-smooth bump in infinite dimensions
cites work: Smooth variational principles with constraints
cites work: On the range of the derivative of a real-valued function with bounded support
cites work: Bump Functions with Hölder Derivatives
cites work: Smooth functions on \(c_0\)
cites work: The Darboux property for gradients
cites work: Local inversion for differentiable functions and the Darboux property
full work available at URL: https://doi.org/10.1007/bf02786693
OpenAlex ID: W2061119501
description: scientific article; zbMATH DE number 2164543