A characterization of weakly sequentially complete Banach lattices
The equivalence of the two following properties is proved for every Banach lattice :1) is weakly sequentially complete.2) Every -Borel measurable linear functional on is -continuous.
A complement of positive weak almost Dunford-Pettis operators on Banach lattices
In this paper, we give some necessary and sufficient conditions such that each positive operator between two Banach lattices is weak almost Dunford-Pettis, and we derive some interesting results about the weak Dunford-Pettis property in Banach lattices.
A Continuity Theorem for Order Bounded Linear Functionals.
A Corson compact L-space from a Suslin tree
The completion of a Suslin tree is shown to be a consistent example of a Corson compact L-space when endowed with the coarse wedge topology. The example has the further properties of being zero-dimensional and monotonically normal.
A density theorem for locally convex lattices.
A Ford-Fulkerson type theorem concerning vector-valued flows in infinite networks
A generalisation of a theorem of Koldunov with an elementary proof
We generalize a Theorem of Koldunov [2] and prove that a disjointness proserving quasi-linear operator between Resz spaces has the Hammerstein property.
A Lagrange multiplier theorem and a sandwich theorem for convex relations.
A new concept of separation
A New Proof of Nakano's Theorem in Locally Solid Riesz Spaces.
A note on direct sum of ordered topological vector spaces
A Note on Extreme Positive Definite Matrices.
A note on L-Dunford-Pettis sets in a topological dual Banach space
The present paper is devoted to some applications of the notion of L-Dunford-Pettis sets to several classes of operators on Banach lattices. More precisely, we establish some characterizations of weak Dunford-Pettis, Dunford-Pettis completely continuous, and weak almost Dunford-Pettis operators. Next, we study the relationships between L-Dunford-Pettis, and Dunford-Pettis (relatively compact) sets in topological dual Banach spaces.
A Note on the Approximation of Elements in the Riesz Tensor Product.
A Note on the Hyperstonian ßX.
A quick and simple proof of Sherman's theorem on order in -algebras.
A short proof on lifting of projection properties in Riesz spaces
Let be an Archimedean Riesz space with a weak order unit . A sufficient condition under which Dedekind [-]completeness of the principal ideal can be lifted to is given (Lemma). This yields a concise proof of two theorems of Luxemburg and Zaanen concerning projection properties of -spaces. Similar results are obtained for the Riesz spaces , , of all functions of the th Baire class on a metric space .
A simplified proof of the Daniell integral extension theorem in ordered spaces
A spectral theory for order unit spaces
A Stone-Weierstrass theorem for Banach lattices