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

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
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