On Carathéodory vector lattices
On Co-Semigroups of Lattice Homomorphisms on a Banach Lattice.
On De Blasi's differentiation theory for multifunctions
On differences of Riesz homomorphisms.
On extensions of orthosymmetric lattice bimorphisms
In the paper we prove that every orthosymmetric lattice bilinear map on the cartesian product of a vector lattice with itself can be extended to an orthosymmetric lattice bilinear map on the cartesian product of the Dedekind completion with itself. The main tool used in our proof is the technique associated with extension to a vector subspace generated by adjoining one element. As an application, we prove that if is a commutative -algebra and its Dedekind completion, then, can be equipped...
On Fixed Point Theorems of Maia Type
On Global Central Decomposition for a Universal Cap.
On invariant elements for positive operators.
In the paper we study the existence of nonzero positive invariant elements for positive operators in Riesz spaces. The class of Riesz spaces for which the results are valid is large enough to contain all the Banach lattices with order continuous norms. All the results obtained in earlier works deal with positive operators in KB-spaces and in many of them the approach is based upon the use of Banach limits. The methods created for KB-spaces cannot be extended to our more general setting; that is...
On Lattice Properties of the Composition Operator.
On lattices and algebras of simple functions
On Lavine's formula for time-delay.
On linear topological Riesz spaces without convexity conditions.
On locally solid topological lattice groups
Let be a commutative Hausdorff locally solid lattice group. In this paper we prove the following: (1) If has the (iii)-property, then its completion is an order-complete locally solid lattice group. (2) If is order-complete and has the Fatou property, then the order intervals of are -complete. (3) If has the Fatou property, then is order-dense in and has the Fatou property. (4) The order-bound topology on any commutative lattice group is the finest locally solid topology on...
On matrices having an invariant cone
On M-ideals and the Alfsen-Effros structure topology.
On Order and Topological Completeness.
On random variables having values in a vector lattice
On Riesz homomorphisms in unital -algebras
The main topic of the first section of this paper is the following theorem: let be an Archimedean -algebra with unit element , and a Riesz homomorphism such that for all . Then every Riesz homomorphism extension of from the Dedekind completion of into itself satisfies for all . In the second section this result is applied in several directions. As a first application it is applied to show a result about extensions of positive projections to the Dedekind completion. A second application...
On Riesz homomorphisms in von Neumann regular f-algebra.
On sequences in vector lattices
In this paper we investigate conditions for a system of sequences of elements of a vector lattice; analogous conditions for systems of sequences of reals were studied by D. E. Peek.