The generalization of total ordering cones and vectorization to separable Hilbert spaces

The characterization of total ordering cones of Rn was given with some properties and optimality conditions in Küçük et al. (2011) [1]. In addition, total ordering cones were used to derive a vector valued function from a special class of set valued mappings in Küçük et al. (2012) [2]. In this study, we give a method for construction of a total ordering cone in a separable Hilbert space by using an orthogonal base. Moreover, we show that every total order can be represented by such a cone. The relationship between the notion of total ordering cone and the notion of vectorization of some set valued mappings are given and some results are obtained.