7 papers · 1 filter
Strong completeness of Lp-type vector lattices
Youssef Azouzi
Let E be a Dedekind complete Riesz space with weak unit e, equipped with a conditional expectation operator T. We prove that the spaces Lp(T), with their natural vector-valued norm…
Order denseness in free Banach lattices
Youssef Azouzi, Wassim Dhifaoui
We prove a fundamental property: the free vector lattice over a Banach space E is order dense in the free p-convex Banach lattice if…
Generating functions in Riesz spaces
Youssef Azouzi, Youssef Nasri
We introduce and study the concept of generating function for natural elements in a Dedekind complete Riesz space equipped with a conditional expectatnion operator. This allows to…
The sup-completion of a Dedekind complete vector lattice
Youssef Azouzi, Youssef Nasri
Every Dedekind complete Riesz space X has a unique sup-completion X^{s}, which is a Dedekind complete lattice cone. This paper aims to present a systematic study this cone by exten…
Burkholder Theorem in Riesz spaces
Youssef Azouzi, Kawtar Ramdane
The main purpose of this paper is to give a vector lattice version of a Theorem by Burkholder about convergence of martingales. The proof is based on a vector lattice analogue of A…
Compact operators between lattice normed spaces
Youssef Azouzi, Mohamed Amine Ben Amor
In this paper we continue the study of compact-like operators in lattice normed spaces started recently by Aydin, Emelyanov, Erkurşun Özcand and Marabeh. We show among others, that…