Mohamed Amine Ben Amor

Associate Professor of Mathematics, University of Carthage (IPEST)
Agrégé Professor of Mathematics, France
Research Group on Ordered Structures with Applications (RGOSA)

Email: mohamedamine.benamor@ipest.rnu.tn

About me

I am an Associate Professor of Mathematics at the University of Carthage (IPEST), Tunisia, and an Agrégé Professor of Mathematics in France.

My research is mainly concerned with ordered functional analysis, Riesz spaces, operator theory, ordered algebraic structures, ergodic theory, and measure-free probability.

A central part of my current research concerns conditional analysis on Riesz spaces, in particular the conditional (L^2(T)) framework developed by Kuo, Labuschagne, and Watson. In this setting, conditional expectation is represented by a positive conditional expectation operator (T), and the usual scalar Hilbert-space geometry is replaced by a geometry taking values in the (f)-algebra (R(T)).

My recent work aims at developing the functional-analytic tools required in this setting: adjoint operators, operator theory, variational methods, Lax–Milgram and Babuška–Nečas theorems, least-squares problems, Tikhonov regularization, and kernel methods.

A new direction of this program concerns approximation theory and artificial intelligence in infinite-dimensional ordered spaces, with the objective of developing a theory of neural networks and universal approximation in conditional (L^2(T))-spaces.

I collaborate closely with Bruce A. Watson (University of the Witwatersrand), as well as with Wen-Chi Kuo and several researchers in France, Tunisia, South Africa, and Europe.

Research interests

Riesz spaces and ordered functional analysis
Positive operators and operator theory
Conditional (L^p(T))-spaces
Measure-free probability and conditional expectations
Ergodic theory in Riesz spaces
Ordered algebraic structures and (f)-algebras
Riesz tensor products
Almost (f)-algebras and (d)-algebras
Pre-Riesz spaces and order compact operators
Variational methods in conditional Hilbert spaces
Kernel methods and regularization
Approximation theory in ordered spaces
Infinite-dimensional machine learning
Neural networks and universal approximation

Current research

Conditional operator theory on (L^2(T))

One of my current projects is the development of an operator theory for conditional (L^2(T))-spaces. This includes the existence and properties of adjoint operators, regular operators, order structures on spaces of operators, and the comparison between order and spectral constructions.

Variational methods

I am developing conditional versions of the Lax–Milgram and Babuška–Nečas theorems. The purpose is to obtain existence, uniqueness, and stability results for variational problems when the underlying Hilbert geometry takes values in (R(T)). This also leads naturally to conditional Petrov–Galerkin methods.

Least squares, Tikhonov regularization and kernel methods

Another part of the program concerns inverse problems and learning. The objective is to develop least-squares methods, Tikhonov regularization, and kernel methods directly in conditional (L^2(T))-spaces.

This provides a bridge between ordered functional analysis and infinite-dimensional learning problems.

Approximation theory and neural networks

I am currently developing an approximation-theoretic approach to neural networks in the conditional setting.

The main question is whether suitable classes of neural networks are dense in natural conditional function spaces. The objective is to obtain conditional analogues of universal approximation results while preserving the intrinsic Riesz-space structure of the problem.

Tensor products and ordered algebras

Tensor products of ordered structures constitute another long-standing part of my research.

My recent work includes tensor products of almost (f)-algebras and questions concerning the extension of algebraic structures to Dedekind completions. This continues my earlier work on tensor products of (f)-algebras, (f)-rings, and (d)-algebras.

Pre-Riesz spaces and compactness

With Youssef Azouzi, Onno van Gaans, and Anke Kalauch, I also work on pre-Riesz spaces, lattice-normed spaces, and order compact operators.

The objective is to understand compactness phenomena before passing to a vector lattice cover and their relationship with compact operators on lattice-normed spaces.

Recent preprints and ongoing work

Adjoints, Order and Spectral Moduli on (L^2(T)), 2026.
Adjoint operators, regular operators, Riesz–Kantorovich modulus, and spectral constructions in conditional (L^2(T))-spaces.
Lax–Milgram and Babuška–Nečas Theorems on Conditional (L^2(T))-Spaces, 2026.
Variational methods and Petrov–Galerkin theory in an (R(T))-valued Hilbert setting.
Conditional Tikhonov Regularization and Kernel Methods on (L^2(T)), 2026.
Least squares, regularization, and kernel methods in the conditional framework.
Approximation Theory and Neural Networks on Conditional (L^2(T))-Spaces, work in progress, 2026.
Approximation and density problems related to infinite-dimensional neural networks and conditional universal approximation.
Tensor Products of Almost (f)-Algebras, 2026.
Riesz tensor products of Archimedean almost (f)-algebras and compatibility of tensor multiplication with the order structure.
Y. Azouzi, M. A. Ben Amor, O. van Gaans and A. Kalauch, Pre-Riesz Spaces as Lattice-Normed Spaces and Order Compact Operators, preprint, 2026.

Selected publications

Y. Azouzi, M. A. Ben Amor, D. Chérif and M. Masmoudi, Conditional supremum in Riesz spaces and applications, Journal of Mathematical Analysis and Applications, 531 (2024).
M. A. Ben Amor, Y. Azouzi, M. Masmoudi and B. A. Watson, The Kac formula and Poincaré recurrence theorem in Riesz spaces, Proceedings of the American Mathematical Society.
M. A. Ben Amor, J. Homann, W.-C. Kuo and B. A. Watson, Characterisation of conditional weak mixing via ergodicity of the tensor product in Riesz spaces, Journal of Mathematical Analysis and Applications, 524 (2023), 127074.
M. A. Ben Amor and A. Omrani, Chernoff’s inequality in Riesz spaces, Quaestiones Mathematicae, 46 (2023), 1761–1776.
M. A. Ben Amor and Y. Azouzi, On compact operators between lattice normed spaces, in Positivity and its Applications, 2021.
M. A. Ben Amor, The Riesz tensor product of d-algebras, Quaestiones Mathematicae, 44 (2021).
M. A. Ben Amor, Tensor product of f-rings, Positivity, 25 (2021).
K. Boulabiar, J. Jaber and M. A. Ben Amor, Orthosymmetric Archimedean-Valued Vector Lattices, in Positivity and Noncommutative Analysis, 2019.
M. A. Ben Amor, J. Jaber and Y. Azouzi, The tensor product of f-algebras, Quaestiones Mathematicae, 41 (2018).
M. A. Ben Amor and Y. Azouzi, On von Neumann regular elements in f-rings, Algebra Universalis, 2017.

RGOSA and scientific activities

I am one of the organizers of the Research Group on Ordered Structures with Applications (RGOSA).

The group brings together researchers working on ordered structures and their applications and develops collaborations between Europe, North Africa, and South Africa.

I am particularly involved in the organization of the RGOSA international seminar and of the Conference on Ordered Structures and Applications (COSA).

COSA is a regular international meeting bringing together researchers in ordered functional analysis, operator theory, probability, ergodic theory, and related areas.

Recent scientific events that I have organized or co-organized include:

COSA 2026, CIRM, Luminy, Marseille, France.
COSA 2025, South Africa.
CIMPA School – Ordered Structures with Applications in Finance and Machine Learning, Sousse, Tunisia, 2024.
COSA 2024, Kenitra, Morocco.
COSA 2023, Tozeur, Tunisia.
Several workshops and schools on ordered spaces, functional analysis, finance, and applications since 2017.

I also contribute to the development and maintenance of the RGOSA scientific network and its web presence.

Teaching and academic experience

I have taught mathematics at all university levels, from undergraduate courses to Master’s programs and preparation for the French Agrégation.

My teaching includes analysis, linear and bilinear algebra, functional analysis, probability, scientific computing, numerical methods, mathematical modelling, and related subjects.

At Université Paris-Dauphine Tunis, I taught mathematics at different levels and held several academic and administrative responsibilities, including Head of the Mathematics Department.

I participated in the creation and development of new programs, in particular programs in Actuarial Science and Big Data.

During the 2025–2026 academic year, I taught at the University of Poitiers in the second year of the Computer Science program, including tutorials in logic and geometry.

During the 2026–2027 academic year, I also teach students in the MP* and PSI* preparatory classes at Lycée Descartes in Tours.

Technology and machine learning education

I was involved for several years in the development of Holberton School Tunis and in technology education.

From 2021 to 2025, I served as Head of the Machine Learning Speciality for the international Holberton network, covering campuses in 21 countries.

This experience strengthened my interest in the mathematical foundations of machine learning and contributed to my current research program on approximation theory, kernel methods, and neural networks in infinite-dimensional ordered spaces.

Education

2020 – Agrégation spéciale de mathématiques, France.
2013 – PhD in Mathematics, University of Tunis El Manar.
2008 – Agrégation de mathématiques, University of Carthage.
2006 – Maîtrise de Mathématiques, Université Paris-Sud, Orsay.
2000–2002 – École Polytechnique, Palaiseau.
1998–2000 – Classes préparatoires, Lycée Louis-le-Grand, Paris.

Selected invited talks

2024 – LSAA Focus Week 2, Madrid: Tensor Product of Bands and Ideals with Applications.
2023 – Positivity XI, Ljubljana: Tensor Product of Riesz Subspaces with Applications.
2022 – Operator Theory 28, Timișoara: Compact-like Operators: Answers to Open Problems.
2019 – Dresden: Compact-like Operators on Lattice-normed Spaces.
2015 – Positivity 9, Chengdu.
2013 – Positivity 8, Leiden.
2013 – International conference in Vladikavkaz.
2011 – Conference on Ordered Spaces and Applications, Athens.

Research collaborations

My research is developed through an international network of collaborations, in particular with researchers in Tunisia, France, South Africa, Germany, the Netherlands, and other European countries.

Current collaborations include work with Bruce A. Watson, Wen-Chi Kuo, Youssef Azouzi, Jamel Jaber, Onno van Gaans, Anke Kalauch, Emmanuel Lépinette, Amal Omrani, and other members of the RGOSA network.

Contact

Mohamed Amine Ben Amor
Associate Professor of Mathematics
University of Carthage – IPEST
Tunisia / France