Representable Monotone Operators and Limits of Sequences of Maximal Monotone Operators

Yboon García; Marc Lassonde

doi:10.1007/s11228-011-0178-8

Representable Monotone Operators and Limits of Sequences of Maximal Monotone Operators

Yboon García, Marc Lassonde

Research output: Contribution to journal › Article in a journal › peer-review

3 Scopus citations

Abstract

We show that the lower limit of a sequence of maximal monotone operators on a reflexive Banach space is a representable monotone operator. As a consequence, we obtain that the variational sum of maximal monotone operators and the variational composition of a maximal monotone operator with a linear continuous operator are both representable monotone operators.

Original language	English
Pages (from-to)	61-73
Number of pages	13
Journal	Set-Valued and Variational Analysis
Volume	20
Issue number	1
DOIs	https://doi.org/10.1007/s11228-011-0178-8
State	Published - 1 Mar 2012
Externally published	Yes

Keywords

Fitzpatrick function
Monotone operator
Sequence of operators
Variational sum

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10.1007/s11228-011-0178-8

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abstract = "We show that the lower limit of a sequence of maximal monotone operators on a reflexive Banach space is a representable monotone operator. As a consequence, we obtain that the variational sum of maximal monotone operators and the variational composition of a maximal monotone operator with a linear continuous operator are both representable monotone operators.",

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AU - Lassonde, Marc

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N2 - We show that the lower limit of a sequence of maximal monotone operators on a reflexive Banach space is a representable monotone operator. As a consequence, we obtain that the variational sum of maximal monotone operators and the variational composition of a maximal monotone operator with a linear continuous operator are both representable monotone operators.

AB - We show that the lower limit of a sequence of maximal monotone operators on a reflexive Banach space is a representable monotone operator. As a consequence, we obtain that the variational sum of maximal monotone operators and the variational composition of a maximal monotone operator with a linear continuous operator are both representable monotone operators.

KW - Fitzpatrick function

KW - Monotone operator

KW - Sequence of operators

KW - Variational sum

KW - Fitzpatrick function

KW - Monotone operator

KW - Sequence of operators

KW - Variational sum

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EP - 73

JO - Set-Valued Analysis

JF - Set-Valued Analysis

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ER -

Representable Monotone Operators and Limits of Sequences of Maximal Monotone Operators

Abstract

Keywords

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