Bot, Radu Ioan ; Grad, Sorin Mihai ; Wanka, Gert : Maximal monotonicity for the precomposition with a linear operator

Author(s):

Bot, Radu Ioan
Grad, Sorin Mihai
Wanka, Gert

Title:

Maximal monotonicity for the precomposition with a linear operator

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 10, 2005

Mathematics Subject Classification:

47H05			[ Monotone operators ]
42A50			[ Conjugate functions, conjugate series, singular integrals ]
90C25			[ Convex programming ]

Abstract:

We give the weakest constraint qualification known to us that assures the maximal monotonicity of the operator A^*o T o 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 assures the maximal monotonicity of the sum of two maximal monotone operators on a reflexive Banach space. Then we give a weak constraint qualification assuring the Brezis-Haraux-type approximation of the range of the subdifferential of the precomposition to A of a proper convex lower-semicontinuous function in non-reflexive Banach spaces, extending and correcting in a special case an older result due to Riahi.

Keywords:

maximal monotone operator, Fitzpatrick function, subdifferential, Brezis-Haraux-type approximation

Language:

English

Publication time:

8 / 2005