Nonlinear monotone operators with values in \({\mathcal L}(X,Y)\)
type: Item
instance of: scholarly article
title: Nonlinear monotone operators with values in \({\mathcal L}(X,Y)\)
zbMATH Open document ID: 0712.47047
DOI: 10.1016/0022-247X(89)90095-4
author: D. Kharzeev
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: let X be a topological vector space, Y an ordered TVS and L(X,Y) the space of continuous linear operators from X into Y. A multivalued operator, \(T:{\mathcal D}(T)\subset X\to Y\), is monotone if \((A_ 1-A_ 2)(x_ 1-x_ 2)\geq 0\) for all \(x_ i\in {\mathcal D}(T)\) and \(A_ i\in T(x_ i)\), \(i=1,2\). In the case \(Y={\mathbb{R}}\), we recover the usual notion of monotone operators. The present situation is motivated and illustrated by the study of subdifferentials of convex functions from X into Y. The main result deals with the upper demicontinuity, upper hemicontinuity and local boundedness of monotone operators from X into Y. Under some restrictions on Y, it is also shown that the subdifferential of a convex operator, \(F:X\to Y\), which has a closed epigraph is a maximum monotone operator.
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47H04
zbMATH DE Number: 4171776
zbMATH Keywords: multivalued operator
zbMATH Keywords: subdifferentials of convex functions
zbMATH Keywords: upper demicontinuity
zbMATH Keywords: upper hemicontinuity
zbMATH Keywords: local boundedness of monotone operators
zbMATH Keywords: maximum monotone operator
MaRDI profile type: Publication
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full work available at URL: 0022-247x(89)90095-4
OpenAlex ID: W2005911912
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description: scientific article; zbMATH DE number 4171776