111 citations · 483 across the 43 of their papers we have counts for
26 papers · 1 filter
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…
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…
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 for a compact space , supplied with the Arens product, is isometrically isomorphic as a Banach algebra to $\mathrm C(\tilde X)…
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…
Spectral theorems for positive algebra homomorphisms
Marcel de Jeu, Xingni Jiang
Let be a locally compact Hausdorff space, let be a partially ordered algebra, and let be a positive algebra homomorphism. Under con…
Riesz representation theorems for positive linear operators
Marcel de Jeu, Xingni Jiang
We generalise the Riesz representation theorems for positive linear functionals on and , where is a locally compact Hausd…
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 . The monotone c…
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…
Convergence structures and locally solid topologies on vector lattices of operators
Yang Deng, Marcel de Jeu
For vector lattices and , where is Dedekind complete and supplied with a locally solid topology, we introduce the corresponding locally solid absolute strong operator to…
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…
Free vector lattices over vector spaces as function lattices
Marcel de Jeu
We show that a free vector lattice over a real vector space can be realised canonically as a vector lattice of real-valued positively homogeneous functions on any linear subspa…
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…
Lattice homomorphisms in harmonic analysis
H. Garth Dales, Marcel de Jeu
Let be a non-empty, closed subspace of a locally compact group that is a subsemigroup of . Suppose that , and are Banach lattices that are vector sublattices o…
On order continuous duals of vector lattices of continuous functions on resolvable spaces
Marcel de Jeu, Jan Harm van der Walt
A topological space is called resolvable if it contains a dense subset with dense complement. Using only basic principles, we show that whenever the space has a resolving s…
Simultaneous power factorization in modules over Banach algebras
Marcel de Jeu, Xingni Jiang
Let be a Banach algebra with a bounded left approximate identity , let be a continuous representation of on a Banach space , and let be a non-em…
Amenable crossed product Banach algebras associated with a class of -dynamical systems
Marcel de Jeu, Rachid El Harti, Paulo R. Pinto
We prove that the crossed product Banach algebra that is associated with a -dynamical system is amenable if is a discrete amenable gr…
Positive representations of . I
Marcel de Jeu, Frejanne Ruoff
We introduce the notion of a positive spectral measure on a -algebra, taking values in the positive projections on a Banach lattice. Such a measure generates a bounded positive…
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 and a class of continuous covariant representat…
Crossed products of Banach algebras. II
Marcel de Jeu, Miek Messerschmidt, Marten Wortel
In earlier work a crossed product of a Banach algebra was constructed from a Banach algebra dynamical system and a class of continuous covariant representat…
A strong open mapping theorem for surjections from cones onto Banach spaces
Marcel de Jeu, Miek Messerschmidt
We show that a continuous additive positively homogeneous map from a closed not necessarily proper cone in a Banach space onto a Banach space is an open map precisely when it is su…
Noncommutative spectral synthesis for the involutive Banach algebra associated with a topological dynamical system
Marcel de Jeu, Jun Tomiyama
If X is a compact Hausdorff space, supplied with a homeomorphism, then a crossed product involutive Banach algebra is naturally associated with these data. If X consists of one poi…
Compact groups of positive operators on Banach lattices
Marcel de Jeu, Marten Wortel
In this paper we study groups of positive operators on Banach lattices. If a certain factorization property holds for the elements of such a group, the group has a homomorphic imag…
Positive representations of finite groups in Riesz spaces
Marcel de Jeu, Marten Wortel
In this paper, which is part of a study of positive representations of locally compact groups in Banach lattices, we initiate the theory of positive representations of finite group…
Crossed products of Banach algebras. I
Sjoerd Dirksen, Marcel de Jeu, Marten Wortel
We construct a crossed product Banach algebra from a Banach algebra dynamical system and a given uniformly bounded class of continuous covariant Banach space represen…