In a nonreflexive space the subdifferential is not onto
type: Item
instance of: scholarly article
title: In a nonreflexive space the subdifferential is not onto
zbMATH Open document ID: 0551.46024
DOI: 10.1007/BF01168159
author: Simon Fitzpatrick
author: Bruce D. Calvert
published in: Mathematische Zeitschrift
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173600
review text: This paper extends the theorem of R. C. James that a Banach space X is reflexive if and only if each continuous linear functional attains its supremum on the unit ball. The result is that for \(\phi\) a lower semicontinuous convex function on X with the interior of its domain nonempty, \(\partial \phi\) is surjective iff for all g in \(X^*\), the function g-\(\phi\) is bounded above and X is reflexive. The paper asks: If \(A:X\to X^*\) is a monotone operator with \(R(A)=X^*\) and int D(A)\(\neq \Phi\), must X be reflexive?
Mathematics Subject Classification ID: 46G05
Mathematics Subject Classification ID: 46B10
Mathematics Subject Classification ID: 47H05
zbMATH DE Number: 3877796
zbMATH Keywords: lower semicontinuous convex function
zbMATH Keywords: monotone operator
MaRDI profile type: Publication
cites work: Differentiability of Lipschitzian mappings between Banach spaces
cites work: Nonlinear integral equations and systems of Hammerstein type
cites work: Opérateurs monotones non linéaires dans les espaces de Banach non réflexifs. (Nonlinear monotone operators on nonreflexive Banach spaces)
cites work: Reflexivity and the sup of linear functionals
cites work: On approximation of approximately linear mappings by linear mappings
OpenAlex ID: W2000900973
description: scientific article; zbMATH DE number 3877796