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Monotone operators, subdifferentials and Asplund spaces

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Part of the Lecture Notes in Mathematics book series (LNM, volume 1364)

Abstract

A set-valued map T from a Banach space E into the subsets of its dual E* is said to be a monotone operator provided
$$ \left\langle {x* - y*,x - y} \right\rangle \geqslant 0 $$
whenever x, yE and x* ∈ T(x), y* ∈ T(y). We do not require that T(x) be nonempty. The domain (or effective domain) D(T) of T is the set of all xE such that T(x) is nonempty.

Keywords

Banach Space Monotone Operator Maximal Monotone Equivalent Norm Maximal Monotone Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

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