6 papers
A Johnson-Kist type representation for truncated vector lattices
Karim Boulabiar, Rawaa Hajji
We introduce the notion of (maximal) multi-truncations on a vector lattice as a generalization of the notion of truncations, an object of recent origin. We obtain a Johnson-Kist ty…
Evaluating characterizations of homomorphisms on truncated vector lattices of functions
Karim Boulabiar, Sameh Bououn
Let be a (non necessarily unital) truncated vector lattice of real-valued functions on a nonempty set . A nonzero linear functional on is called a truncation homomor…
Orthosymmetric spaces over an Archimedean vector lattice
Mohamed Amine Ben Amor, Karim Boulabiar, Jamel Jaber
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…
Lattice norms on the unitization of a truncated normed Riesz space
Karim Boulabiar, Hamza Hafsi
Truncated Riesz spaces was first introduced by Fremlin in the context of real-valued functions. An appropriate axiomatization of the concept was given by Ball. Keeping only the fir…
Unitization of a lattice ordered ring with a truncation
Karim Boulabiar, Mounir Mahfoudhi
Let be a lattice ordered ring along with a truncation in the sense of Ball. We give a necessary and sufficient condition on for its unitization to be ag…
Representation of strongly truncated Riesz spaces
Karim Boulabiar, Rawaa Hajji
Following a recent idea by Ball, we introduce the notion of strongly truncated Riesz space with a suitable spectrum. We prove that, under an extra Archimedean type condition, any s…