Tensor Products of Banach Lattices.
The -weak compactness of weak Banach-Saks operators
We characterize Banach lattices on which every weak Banach-Saks operator is b-weakly compact.
The boundedness principle for lattice-normed spaces.
The Components of a Positive Operator.
The dual of the cone of all convex functions on a vector space.
The Dual of the Cone of All Convex Functions on a Vector Space. (Short Communication).
The equivalence of Boolean prime ideal theorem and a theorem of functional analysis
The facial structure of the finite dimensional latticial cone.
The Generalized Theory of Perfect Riesz Spaces I.
The Hahn-Banach property and equivalent conditions
The injective hull of an archimedean f-algebra
The measure extension problem for vector lattices
Let be a boundedly -complete vector lattice. If each -valued premeasure on an arbitrary field of subsets of an arbitrary set can be extended to a -additive measure on the generated -field then is said to have the measure extension property. Various sufficient conditions on which ensure that it has this property are known. But a complete characterisation of the property, that is, necessary and sufficient conditions, is obtained here. One of the most useful characterisations is: has the...
The order -complete vector lattice of AM-compact operators
We establish necessary and sufficient conditions under which the linear span of positive AM-compact operators (in the sense of Fremlin) from a Banach lattice into a Banach lattice is an order -complete vector lattice.
The semi- property for normed Riesz spaces
The space of maximal convex sets
The Stieltjes moment problem in vector lattices.
The uniform boundedness principle for order bounded operators.
The weak compactness of almost Dunford-Pettis operators
We characterize Banach lattices on which every positive almost Dunford-Pettis operator is weakly compact.
The -property in
The -property of a Riesz space (real vector lattice) is: For each sequence of positive elements of , there is a sequence of positive reals, and , with for each . This condition is involved in studies in Riesz spaces of abstract Egoroff-type theorems, and of the countable lifting property. Here, we examine when “” obtains for a Riesz space of continuous real-valued functions . A basic result is: For discrete , has iff the cardinal , Rothberger’s bounding number. Consequences and...
Theorems of the alternative for cones and Lyapunov regularity of matrices
Standard facts about separating linear functionals will be used to determine how two cones and and their duals and may overlap. When is linear and and are cones, these results will be applied to and , giving a unified treatment of several theorems of the alternate which explain when contains an interior point of . The case when is the space of Hermitian matrices, is the positive semidefinite matrices, and yields new and known results about the existence of block diagonal...