Natural closures, natural compositions and natural sums of monotone operators
type: Item
instance of: scholarly article
title: Natural closures, natural compositions and natural sums of monotone operators
zbMATH Open document ID: 1147.47037
author: Jean-Paul Penot
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2008-06-24T00:00:00Z
review text: The author presents the natural topology \(\nu\) on the product \(X\times X^*\) of a Banach space with its dual space, and studies the properties of monotone operators in this topology. Then he defines the following generalized operations: the natural / fuzzy / natural extended / natural variational composition of an operator \(M:Y\rightrightarrows Y^*\) with a linear operator \(A:X\to Y\), and the natural / fuzzy sum of two operators \(M,\,N:X\rightrightarrows X^*\), where \(X,\,Y\) are Banach spaces. Their properties (pointing out the case of monotone operators) and connections between them and other notions or previous constructions by Attouch-Baillon-Théra, Revalski-Théra and Pennanen-Revalski-Théra are investigated in this paper.
reviewed by: Rodica Luca
Mathematics Subject Classification ID: 47H05
zbMATH DE Number: 5292200
zbMATH Keywords: asymptotic analysis
zbMATH Keywords: composition
zbMATH Keywords: fuzzy sum
zbMATH Keywords: monotone operator
MaRDI profile type: Publication
full work available at URL: j.matpur.2008.02.001
OpenAlex ID: W4310648742
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Natural closures, natural compositions and natural sums of monotone operators (cites work)
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Natural closures, natural compositions and natural sums of monotone operators (DOI)
DOI: 10.1016/J.MATPUR.2008.02.001