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Mohamed Amine Ben Amor

Publications and source records attributed to Mohamed Amine Ben Amor.

14 recordsLinked to original sources
arXiv2026

A $d$-algebra whose product does not extend to its Dedekind completion

We construct a Banach lattice $d$-algebra with a strong order unit whose product has no positive associative bilinear extension to its Dedekind completion. This gives a negative answer to a question of Wickstead and to the $d$-algebra case of a question of Huijsmans. It also disproves an extension theorem of Chil. The example shows that norm completeness and a strong order unit do not ensure that multiplication extends to the Dedekind completion.

math.FA↗
arXiv2026

Tensor Products of Almost \(f\)-Algebras: A Counterexample

We show that the natural tensor product multiplication of two Archimedean almost \(f\)-algebras does not, in general, extend to their Fremlin tensor product. The two algebras in the counterexample have the same underlying vector lattice \(C[0,1]\). Their multiplications are explicit, positive and nilpotent of index three. The obstruction is the fact that the function \((s,t)\mapsto e^{st}\) does not belong to \(C[0,1]\ftensor C[0,1]\). The same construction gives Banach almost \(f\)-algebras and has consequences for previously published assertions on Riesz and Fremlin projective tensor products of almost \(f\)-algebras.

math.FA↗
arXiv2026

Conditional expectation operators on $C(X)$

At the COSAEF conference in 2021, several participants asked the question whether a conditional expectation operator in the sense of Kuo, Labaushagne and Watson could be constructed in vector lattices other than $\mathcal{L}_p$ spaces and in particular in $C(X)$. This work answers positively to this question and participates in an old discussion on integrals in $C(X)$ space.

math.FA↗
arXiv2026

Adjoints, Order and Spectral Moduli on $L^2(T)$

We study adjoints of $R(T)$-linear, $T$-strongly bounded operators on the conditional space $L^2(T)$ and the interaction between its Hilbert-type geometry and its Riesz-space order. This produces two natural operator moduli: the Riesz--Kantorovich order modulus and the spectral modulus $(S^*S)^{1/2}$. After isolating the $T$-regular operators, we show that they form a Dedekind-complete order ideal in the natural lattice of order-bounded $R(T)$-module homomorphisms. On this operator lattice the order operations remain $T$-strongly bounded and the adjoint is an order automorphism. We then compare the two moduli and explain why they may differ.

math.FA↗
arXiv2023

Tensor products of Bands and Ideals

In this study we give an answer to the open question about the Riesz tensor product of ideals and bands of a Riesz space. We prove among other results that the Dedekind completion of the Riesz tensor product of two ideals is again an ideal.

math.FA↗
arXiv2023

Conditional supremum in Riesz spaces and applications

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 is crucial in generalizing various results across multiple disciplines to the framework of Riesz spaces. Among other applications, we utilize this concept in finance to derive characterizations of certain financial conditions.

math.FA↗
arXiv2022

Characterisation of conditional weak mixing via ergodicity of the tensor product in Riesz Spaces

We link conditional weak mixing and ergodicity of the tensor product in Riesz spaces. In particular, we characterise conditional weak mixing of a conditional expectation preserving system by the ergodicity of its tensor product with itself or other ergodic systems. In order to achieve this we characterise the components of the weak order units in the tensor product of two Dedekind complete Riesz spaces with weak order units.

math.FA↗
arXiv2022

The Kac formula and Poincaré recurrence theorem in Riesz spaces

Riesz space (non-pointwise) generalizations for iterative processes are given for the concepts of recurrence, first recurrence and conditional ergodicity. Riesz space conditional versions of the Poincaré Recurrence Theorem and the Kac formula are developed. Under mild assumptions, it is shown that every conditional expectation preserving process is conditionally ergodic with respect to the conditional expectation generated by the Cesàro mean associated with the iterates of the process. Applied to processes in $L^1(Ω,{\mathcal A},μ)$, where $μ$ is a probability measure, new conditional versions of the above theorems are obtained.

math.PR↗
arXiv2020

Concentration Inequalities in Riesz Spaces

In this work, we will generalize the moment generating function to Riesz spaces. We will derive some of its properties and use it to prove concentration inequalities on Riesz spaces.

math.FA↗
arXiv2019

Orthosymmetric spaces over an Archimedean vector lattice

We introduce and study the notion of orthosymmetric spaces over an Archimedean vector lattice as a generalization of finite-dimentional Euclidean inner spaces. A special attention has been paid to linear operators on these spaces.

math.FA↗
arXiv2019

Compact operators between lattice normed spaces

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 every p-compact operator between lattice normed spaces is p-bounded. The paper contains answers of almost all questions asked by these authors.

math.FA↗
arXiv2017

Tensor product of $f$-rings

In this paper we prove that $\ell$-group tensor product of archimedean $f$-rings is an $f$-ring. We will use this result to characterize multiplicative $\ell$-bimorphisms between unital $f$-rings.

math.RA↗
arXiv2015

The tensor product of function algebras

In this paper we study the tensor product of two $f$-algebras. We show that the Riesz Subspace generated by a subalgebra in an $f$-algebra is an algebra in order to prove that the Riesz tensor product of two $f$-algebras has a structure of an $f$-algebra.

math.FA↗