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Domains of accretive operators in Banach spaces

Part of: Nonlinear functional analysis Nonlinear operators and their properties

Published online by Cambridge University Press:  07 January 2016

Jesús Garcia-Falset ,
Omar Muñiz-Pérez  and
Simeon Reich
Jesús Garcia-Falset
Affiliation:
Departament d'Anàlisi Matemàtica, Universitat de València, Dr Moliner 50, 46100 Burjassot, València, Spain (garciaf@uv.es; , omar.muniz@uv.es)
Omar Muñiz-Pérez
Affiliation:
Departament d'Anàlisi Matemàtica, Universitat de València, Dr Moliner 50, 46100 Burjassot, València, Spain (garciaf@uv.es; , omar.muniz@uv.es)
Simeon Reich
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, 32000 Haifa, Israel (sreich@tx.technion.ac.il)
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Extract

Let D(A) be the domain of an m-accretive operator A on a Banach space E. We provide sufficient conditions for the closure of D(A) to be convex and for D(A) to coincide with E itself. Several related results and pertinent examples are also included.

Keywords

accretive operatorBanach spaceduality mappingfixed pointKadec–Klee propertyresolvent

MSC classification

Secondary: 46T99: None of the above, but in this section 47H04: Set-valued operators 47H06: Accretive operators, dissipative operators, etc. 47H10: Fixed-point theorems
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 2 , April 2016 , pp. 325 - 336
Copyright
Copyright © Royal Society of Edinburgh 2016 

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