On a lattice characterization of Hilbert spaces
On a property of Riesz spaces
On a question of Fremlin concerning order bounded and regular operators
On a weak Freudenthal spectral theorem
Let be an Archimedean Riesz space and its Boolean algebra of all band projections, and put and , . is said to have Weak Freudenthal Property () provided that for every the lattice is order dense in the principal band . This notion is compared with strong and weak forms of Freudenthal spectral theorem in Archimedean Riesz spaces, studied by Veksler and Lavrič, respectively. is equivalent to -denseness of in for every , and every Riesz space with sufficiently many projections...
On algebra homomorphisms in complex almost -algebras
Extensions of order bounded linear operators on an Archimedean vector lattice to its relatively uniform completion are considered and are applied to show that the multiplication in an Archimedean lattice ordered algebra can be extended, in a unique way, to its relatively uniform completion. This is applied to show, among other things, that any order bounded algebra homomorphism on a complex Archimedean almost -algebra is a lattice homomorphism.
On an extension of finite functionals by the transfinite induction
On Banach ideals determined by Banach lattices and their applications [Book]
On boundedly order-complete locally solid Riesz spaces
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.