Spaces generated by the cone of sublinear operators

Keywords: Riesz space, Banach lattice, homogeneous operator, sublinear operator, order continuous operator
Published online: 2018-12-31


This paper deals with a study on classes of non linear operators. Let $SL(X,Y)$ be the set of all sublinear operators between two Riesz spaces $X$ and $Y$. It is a convex cone of the space $H(X,Y)$ of all positively homogeneous operators. In this paper we study some spaces generated by this cone, therefore we study several properties, which are well known in the theory of Riesz spaces, like order continuity, order boundedness etc. Finally, we try to generalise the concept of adjoint operator. First, by using the analytic form of Hahn-Banach theorem, we adapt the notion of adjoint operator to the category of positively homogeneous operators. Then we apply it to the class of operators generated by the sublinear operators.

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How to Cite
Slimane A. Spaces Generated by the Cone of Sublinear Operators. Carpathian Math. Publ. 2018, 10 (2), 376-386.