The injective hull of an archimedean f-algebra
The integral analog of a series with a two-point sum range.
The intersection convolution of relations and the Hahn-Banach type theorems
By introducing the intersection convolution of relations, we prove a natural generalization of an extension theorem of B. Rodrí guez-Salinas and L. Bou on linear selections which is already a substantial generalization of the classical Hahn-Banach theorems. In particular, we give a simple neccesary and sufficient condition in terms of the intersection convolution of a homogeneous relation and its partial linear selections in order that every partial linear selection of this relation can have an...
The kernel theorem for Laplace ultradistributions
A kernel theorem for spaces of Laplace ultradistributions supported by an n-dimensional cone of product type is stated and proved.
The Krein-Šmulian theorem and its extension
The Kreps-Yan theorem for Banach ideal spaces.
The Kreps–Yan theorem for .
The L1 Structure of Weak L1.
The Lie algebra of a nuclear group.
The Lindelöf property and σ-fragmentability
In the previous paper, we, together with J. Orihuela, showed that a compact subset X of the product space is fragmented by the uniform metric if and only if X is Lindelöf with respect to the topology γ(D) of uniform convergence on countable subsets of D. In the present paper we generalize the previous result to the case where X is K-analytic. Stated more precisely, a K-analytic subspace X of is σ-fragmented by the uniform metric if and only if (X,γ(D)) is Lindelöf, and if this is the case then...
The Lindelöf property in Banach spaces
A topological space (T,τ) is said to be fragmented by a metric d on T if each non-empty subset of T has non-empty relatively open subsets of arbitrarily small d-diameter. The basic theorem of the present paper is the following. Let (M,ϱ) be a metric space with ϱ bounded and let D be an arbitrary index set. Then for a compact subset K of the product space the following four conditions are equivalent: (i) K is fragmented by , where, for each S ⊂ D, . (ii) For each countable subset A of D, is...
The locally convex -spaces and their dual spaces.
The Lorentz Sequence Spaces d(w, p) Where w is Increasing.
The Mackey completions of some interpolation F-spaces
The Mackey convergence condition for spaces with webs.
The Mackey-Arens and Hahn-Banach theorems for spaces over valued fields
The Mackey-Arens theorem for non-locally convex spaces.
Let R be a subcategory of the category of all topological vector spaces. Let E be an element of R. The problem of the existence of the finest R-topology on E with the same continuous linear functionals as the original one is discussed. Remarks concerning the Hahn-Banach Extension Property are included.
The maximal normal subspace of the inverse image of a normal space of sequences by a non-negative matrix transformation
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 measure of noncompactness of matrix transformations on the spaces and ().