Preprint C149/2012
On non-type (D) operators in non-reflexive Banach spaces and closures of monotone operators in topological vector spaces
Orestes Martin Bueno Tangoa
Keywords: type (D) monotone operators | monotone polar closure | representable closure
In this thesis, we study certain properties of monotone operators in two different contexts. In the first context, we show under which conditions we can construct linear monotone operators which are not of type (D). Moreover, we give negative answers to two conjectures due to Marques-Alves and Svaiter, and Borwein, respectively. In the second context, we study the relationship between the monotone polar closure and the representable closure of a monotone operator in a Hausdorff and locally convex topological vector space. This extends a result due to Mart�nez-Legaz and Svaiter.