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

The characterization of total ordering cones of R n 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.