M. de Jeu

activity

19942024

most citedPaley-Wiener theorems for the Dunkl transform

111 citations · 483 across the 43 of their papers we have counts for

collaborators

47 papers

math.FA2024

Free Banach lattices over pre-ordered Banach spaces

Marcel de Jeu, Xingni Jiang

We study free Banach lattices over pre-ordered Banach spaces in the category of Banach lattices of a given convexity type. These generalise the free Banach lattices under convexity…

math.FA2023

Embedded unbounded order convergent sequences in topologically convergent nets in vector lattices

Yang Deng, Marcel de Jeu

We show that, for a class of locally solid topologies on vector lattices, a topologically convergent net has an embedded sequence that is unbounded order convergent to the same lim…

math.FA2022

The order bidual of C(X) for a realcompact space

Marcel de Jeu, Jan Harm van der Walt

It is well known that the bidual of $C (X)$ for a compact space $X$ , supplied with the Arens product, is isometrically isomorphic as a Banach algebra to $\mathrm C(\tilde X)…

math.FA2022★ 3 cited

Direct limits in categories of normed vector lattices and Banach lattices

Chun Ding, Marcel de Jeu

After collecting a number of results on interval and almost interval preserving linear maps and vector lattice homomorphisms, we show that direct systems in various categories of n…

math.FA2021★ 2 cited

Spectral theorems for positive algebra homomorphisms

Marcel de Jeu, Xingni Jiang

Let $X$ be a locally compact Hausdorff space, let $A$ be a partially ordered algebra, and let $π : C_{c} (X) \to A$ be a positive algebra homomorphism. Under con…

math.FA2021★ 5 cited

Riesz representation theorems for positive linear operators

Marcel de Jeu, Xingni Jiang

We generalise the Riesz representation theorems for positive linear functionals on $C_{c} (X)$ and $C_{0} (X)$ , where $X$ is a locally compact Hausd…

math.FA2021★ 5 cited

Order Integrals

Marcel de Jeu, Xingni Jiang

We define an integral of real-valued functions with respect to a measure that takes its values in the extended positive cone of a partially ordered vector space $E$ . The monotone c…

math.FA2020★ 1 cited

Convergence structures and Hausdorff uo-Lebesgue topologies on vector lattice algebras of operators

Yang Deng, Marcel de Jeu

A vector sublattice of the order bounded operators on a Dedekind complete vector lattice can be supplied with the convergence structures of order convergence, strong order converge…

math.FA2020★ 3 cited

Convergence structures and locally solid topologies on vector lattices of operators

Yang Deng, Marcel de Jeu

For vector lattices $E$ and $F$ , where $F$ is Dedekind complete and supplied with a locally solid topology, we introduce the corresponding locally solid absolute strong operator to…

math.FA2020★ 3 cited

Vector lattices with a Hausdorff uo-Lebesgue topology

Yang Deng, Marcel de Jeu

We investigate the construction of a Hausdorff uo-Lebesgue topology on a vector lattice from a Hausdorff (o)-Lebesgue topology on an order dense ideal, and what the properties of t…

math.FA2020

Free vector lattices over vector spaces as function lattices

Marcel de Jeu

We show that a free vector lattice over a real vector space $V$ can be realised canonically as a vector lattice of real-valued positively homogeneous functions on any linear subspa…

math.FA2020

Free vector lattices and free vector lattice algebras

Marcel de Jeu

We show how the existence of various free vector lattices and free vector lattice algebras can be derived from a theorem on equational classes in universal algebra. A discussion ab…

math.FA2018

Lattice homomorphisms in harmonic analysis

H. Garth Dales, Marcel de Jeu

Let $S$ be a non-empty, closed subspace of a locally compact group $G$ that is a subsemigroup of $G$ . Suppose that $X, Y$ , and $Z$ are Banach lattices that are vector sublattices o…

math.FA2018★ 1 cited

On order continuous duals of vector lattices of continuous functions on resolvable spaces

Marcel de Jeu, Jan Harm van der Walt

A topological space $X$ is called resolvable if it contains a dense subset with dense complement. Using only basic principles, we show that whenever the space $X$ has a resolving s…

math.OA2018★ 2 cited

The structure of doubly non-commuting isometries

Marcel de Jeu, Paulo R. Pinto

Suppose that $n \geq 1$ and that, for all $i$ and $j$ with $1 \leq i, j \leq n$ and $i \neq = j$ , $z_{ij} \in T$ are given such that $z_{j i} = z_{ij}$ for all $i \neq = j$ .…

math.OA2017

The closure of ideals of $ℓ^{1} (Σ)$ in its enveloping $C^{*}$ -algebra

Marcel de Jeu, Jun Tomiyama

If $X$ is a compact Hausdorff space and $σ$ is a homeomorphism of $X$ , then an involutive Banach algebra $ℓ^{1} (Σ)$ of crossed product type is naturally associated with the topolo…

math.FA2016★ 2 cited

Simultaneous power factorization in modules over Banach algebras

Marcel de Jeu, Xingni Jiang

Let $A$ be a Banach algebra with a bounded left approximate identity ${e_{λ}}_{λ \in Λ}$ , let $π$ be a continuous representation of $A$ on a Banach space $X$ , and let $S$ be a non-em…

math.FA2016★ 4 cited

Amenable crossed product Banach algebras associated with a class of $C^{*}$ -dynamical systems

Marcel de Jeu, Rachid El Harti, Paulo R. Pinto

We prove that the crossed product Banach algebra $ℓ^{1} (A, G, α)$ that is associated with a $C^{*}$ -dynamical system $(A, G, α)$ is amenable if $G$ is a discrete amenable gr…

math.OA2016

Nonsimplicity of certain universal $C^{*}$ -algebras

Marcel de Jeu, Rachid El Harti, Paulo R. Pinto

Given $n \geq 2$ , $z_{ij} \in T$ such that $z_{ij} = z_{j i}$ for $1 \leq i, j \leq n$ and $z_{ii} = 1$ for $1 \leq i \leq n$ , and integers $p_{1}, ..., p_{n} \geq 1$ , we show that…

math.FA2015★ 6 cited

Positive representations of $C_{0} (X)$ . I

Marcel de Jeu, Frejanne Ruoff

We introduce the notion of a positive spectral measure on a $σ$ -algebra, taking values in the positive projections on a Banach lattice. Such a measure generates a bounded positive…

math.RT2015★ 8 cited

Disintegration of positive isometric group representations on $L^{p}$ -spaces

Marcel de Jeu, Jan Rozendaal

Let $G$ be a Polish locally compact group acting on a Polish space $X$ with a $G$ -invariant probability measure $μ$ . We factorize the integral with respect to $μ$ in terms of the i…

math.OA2014★ 7 cited

Algebraically irreducible representations and structure space of the Banach algebra associated with a topological dynamical system

Marcel de Jeu, Jun Tomiyama

If $X$ is a compact Hausdorff space and $σ$ is a homeomorphism of $X$ , then a Banach algebra $ℓ^{1} (Σ)$ of crossed product type is naturally associated with this topological dynam…

math.CA2014

Rapid polynomial approximation in $L_{2}$ -spaces with Freud weights on the real line

Rui Xie, Marcel de Jeu

The weights $W_{α} (x) = exp (- ∣ x ∣^{α})$ $(α > 1)$ form a subclass of Freud weights on the real line. Primarily from a functional analytic angle, we investigate the subspace of $L_2(\math…

math.FA2013★ 1 cited

Crossed products of Banach algebras. III

Marcel de Jeu, Miek Messerschmidt

In earlier work a crossed product of a Banach algebra was constructed from a Banach algebra dynamical system $(A, G, α)$ and a class $R$ of continuous covariant representat…

Free Banach lattices over pre-ordered Banach spaces

Embedded unbounded order convergent sequences in topologically convergent nets in vector lattices

The order bidual of C(X) for a realcompact space

Direct limits in categories of normed vector lattices and Banach lattices

Spectral theorems for positive algebra homomorphisms

Riesz representation theorems for positive linear operators

Order Integrals

Convergence structures and Hausdorff uo-Lebesgue topologies on vector lattice algebras of operators

Convergence structures and locally solid topologies on vector lattices of operators

Vector lattices with a Hausdorff uo-Lebesgue topology

Free vector lattices over vector spaces as function lattices

Free vector lattices and free vector lattice algebras

Lattice homomorphisms in harmonic analysis

On order continuous duals of vector lattices of continuous functions on resolvable spaces

The structure of doubly non-commuting isometries

The closure of ideals of ℓ1(Σ) in its enveloping C∗-algebra

Simultaneous power factorization in modules over Banach algebras

Amenable crossed product Banach algebras associated with a class of C∗-dynamical systems

Nonsimplicity of certain universal C∗-algebras

Positive representations of C0​(X). I

Disintegration of positive isometric group representations on Lp-spaces

Algebraically irreducible representations and structure space of the Banach algebra associated with a topological dynamical system

Rapid polynomial approximation in L2​-spaces with Freud weights on the real line

Crossed products of Banach algebras. III

The closure of ideals of $ℓ^{1} (Σ)$ in its enveloping $C^{*}$ -algebra

Amenable crossed product Banach algebras associated with a class of $C^{*}$ -dynamical systems

Nonsimplicity of certain universal $C^{*}$ -algebras

Positive representations of $C_{0} (X)$ . I

Disintegration of positive isometric group representations on $L^{p}$ -spaces

Rapid polynomial approximation in $L_{2}$ -spaces with Freud weights on the real line