Open AccessSpaces generated by the cone of sublinear operators
Author(s) -
Abdelghaffar Slimane
Publication year - 2018
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.10.2.376-386
Subject(s) - mathematics , sublinear function , cone (formal languages) , pure mathematics , operator (biology) , operator theory , nuclear operator , unbounded operator , banach space , order (exchange) , compact operator on hilbert space , class (philosophy) , space (punctuation) , regular polygon , discrete mathematics , finite rank operator , compact operator , extension (predicate logic) , philosophy , algorithm , repressor , artificial intelligence , linguistics , chemistry , computer science , biochemistry , geometry , transcription factor , programming language , finance , economics , gene
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.