Spaces generated by the cone of sublinear operators

Array

Authors

  • A. Slimane Laboratory of functional analysis and geometry of spaces, University of M’sila, M’sila 28000, Algeria https://orcid.org/0000-0001-6870-1442

DOI:

https://doi.org/10.15330/cmp.10.2.376-386

Keywords:

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

Abstract

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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Published

2018-12-31

How to Cite

(1)
Slimane, A. Spaces Generated by the Cone of Sublinear Operators: Array. Carpathian Math. Publ. 2018, 10, 376-386.

Issue

Section

Scientific articles