Positive bases and atomic sublattices
Ioannis A. Polyrakis · 2021
Suppose that the ordering in a vector lattice E is defined by a countable family f_i|i∈𝐍 of positive linear functional of E, i.e. x∈ E_+ iff f_i(x)≥ 0, for any i. Based on the study of the supports of the vectors of E with respect to this family, we examine the existence of atoms in the positive cone of the lattice-subspaces X of E and we give sufficient conditions in order X to be atomic or to have a positive basis. These results have applications in the theory of options (derivatives) in finance.