2 citations · 2 across the 13 of their papers we have counts for
17 papers
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…
A counterexample regarding the relatively uniform completion of a principal ideal
Youssef Azouzi
We present a counterexample related to relative uniform convergence, showing that, in general, the relatve uniform completion of the principal ideal of a vector lattice E generated…
A Kakutani-Rokhlin decomposition for conditionally ergodic process in the measure-free setting of vector lattices
Youssef Azouzi, Marwa Masmoudi, Bruce Alastair Watson
Recently the Kac formula for the conditional expectation of the first recurrence time of a conditionally ergodic conditional expectation preserving system was established in the me…
The sup-completion of a Dedekind complete vector lattice II
Youssef Azouzi, Youssef Nasri
We persist in our investigation of the sup-completion of a Dedekind complete Riesz space, extending to the broader context of Riesz spaces. some results initially obtained by Feng,…
The strong Nakano property in Banach lattices
Youssef Azouzi, Asma Ben Rjeb, Pedro Tradacete
We study the strong Nakano property in Banach lattices with a special focus on free Banach lattices. We show that for every finite dimensional Banach space , the free Banach lat…
Some characterizations of ergodicity in Riesz spaces
Youssef Azouzi, Marwa Masmoudi
In the recent surge of papers on ergodic theory within Riesz spaces, this article contributes by introducing enhanced characterizations of ergodicity. Our work extends and strength…
Uniform Integrability in vector lattices and applications
Youssef Azouzi
In this paper, we explore an abstraction of uniform integrability in vector lattices and demonstrate its application by providing a positive solution to an open question posed by K…
A diagonal principle for nets
Youssef Azouzi
In our work, we provide a constructive proof of a generalized version of Cantor's diagonal argument for nets. This result expands the well-known technique beyond sequences, allowin…
Conditional supremum in Riesz spaces and applications
Youssef Azouzi, Mohamed Amine Ben Amor, Dorsaf Cherif +1
We extend the concept of conditional supremum to the measure-free setting of Riesz spaces via the conditional expectation operator. We explore its properties and show how this tool…
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 Kac formula and Poincaré recurrence theorem in Riesz spaces
Youssef Azouzi, Mohamed Amine Ben Amor, Jonathan Homann +2
Riesz space (non-pointwise) generalizations for iterative processes are given for the concepts of recurrence, first recurrence and conditional ergodicity. Riesz space conditional v…
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…
Completeness for vector lattices
Youssef Azouzi
The notion of unboundedly order converges has been recieved recently a particular attention by several authors. The main result of the present paper shows that the notion is effici…
The tensor product of function algebras
Youssef Azouzi, Mohamed Amine Ben Amor, Jamel Jaber
In this paper we study the tensor product of two -algebras. We show that the Riesz Subspace generated by a subalgebra in an -algebra is an algebra in order to prove that the…