The Sum and Chain Rules for Maximal Monotone Operators

Details The Sum and Chain Rules for Maximal Monotone Operators The Sum and Chain Rules for Maximal Monotone Operators

2006-09-11

arxiv.org/abs/math/0609296v1

Mathematics

Functional Analysis

17 pages, submitted to Set-Valued Analysis

Scientific paper

This paper is primarily concerned with the problem of maximality for the sum $A+B$ and composition $L^{*}ML$ in non-reflexive Banach space settings under qualifications constraints involving the domains of $A,B,M$. Here $X$, $Y$ are Banach spaces with duals $X^{*}$, $Y^{*}$, $A,B:X\rightrightarrows X^{*}$, $M:Y\rightrightarrows Y^{*}$ are multi-valued maximal monotone operators, and $L:X\to Y$ is linear bounded. Based on the Fitzpatrick function, new characterizations for the maximality of an operator as well as simpler proofs, improvements of previously known results, and several new results on the topic are presented.

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