Maximal monotonicity, conjugation and the duality product in non-reflexive Banach spaces
نویسندگان
چکیده
Maximal monotone operators on a Banach space into its dual can be represented by convex functions bounded below by the duality product. It is natural to ask under which conditions a convex function represents a maximal monotone operator. A satisfactory answer, in the context of reflexive Banach spaces, has been obtained some years ago. Recently, a partial result on non-reflexive Banach spaces was obtained. In this work we study some others conditions which guarantee that a convex function represents a maximal monotone operator in non-reflexive Banach spaces. 2000 Mathematics Subject Classification: 47H05, 49J52, 47N10.
منابع مشابه
On the surjectivity properties of perturbations of maximal monotone operators in non-reflexive Banach spaces
We are concerned with surjectivity of perturbations of maximal monotone operators in non-reflexive Banach spaces. While in a reflexive setting, a classical surjectivity result due to Rockafellar gives a necessary and sufficient condition to maximal monotonicity, in a nonreflexive space we characterize maximality using a “enlarged” version of the duality mapping, introduced previously by Gossez....
متن کاملMaximal Monotonicity for the Precomposition with a Linear Operator
We give the weakest constraint qualification known to us that ensures the maximal monotonicity of the operator A∗ ◦ T ◦A when A is a linear continuous mapping between two reflexive Banach spaces and T is a maximal monotone operator. As a special case we get the weakest constraint qualification that ensures the maximal monotonicity of the sum of two maximal monotone operators on a reflexive Bana...
متن کاملLC-functions and maximal monotonicity
In this paper, we consider LC–functions, a class of special convex functions from the product of a reflexive Banach space and its dual into ]−∞,∞]. Using Fitzpatrick functions, we will show that the theory of LC–functions is a proper extension of the theory of maximal monotone sets. Various versons of the Fenchel duality theorem lead to a number of results on maximal monotonicity, some of them ...
متن کاملSSDB spaces and maximal monotonicity
In this paper, we develop some of the theory of SSD spaces and SSDB spaces, and deduce some results on maximally monotone multifunctions on a reflexive Banach space.
متن کاملA new old class of maximal monotone operators
In a recent paper in Journal of Convex Analysis the authors studied, in non-reflexive Banach spaces, a class of maximal monotone operators, characterized by the existence of a function in Fitzpatrick’s family of the operator which conjugate is above the duality product. This property was used to prove that such operators satisfies a restricted version of Brøndsted-Rockafellar property. In this ...
متن کامل