Spaces generated by the cone of sublinear operators

A. Slimane


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 $H(X,Y)$ the space 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. We first adapt by using the analytic form of Hahn-Banach theorem, the notion of adjoint operator to the category of positively homogeneous operators, and then we apply it to the class of operators generated by the sublinear operators.


Riesz space, Banach lattice, homogeneous operator, sublinear operator, order continuous operator.

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