The Generalized Theory of Perfect Riesz Spaces I.
The Gliding Hump Property in Vector Sequence Spaces.
The Gruenhage property, property *, fragmentability, and σ-isolated networks in generalized ordered spaces
We examine the Gruenhage property, property * (introduced by Orihuela, Smith, and Troyanski), fragmentability, and the existence of σ-isolated networks in the context of linearly ordered topological spaces (LOTS), generalized ordered spaces (GO-spaces), and monotonically normal spaces. We show that any monotonically normal space with property * or with a σ-isolated network must be hereditarily paracompact, so that property * and the Gruenhage property are equivalent in monotonically normal spaces....
The Hahn-Banach property and equivalent conditions
The Hahn-Banach theorem implies the Banach-Tarski paradox
The Hahn-Banach theorem implies the existence of a non-Lebesgue measurable set
The Hahn-Banach Theorem surveyed [Book]
The Hahn-Banach-Kantorovich formula for a lattice subdifferential.
The holomorphic functional calculus as an operational calculus
The Hypercyclicity Criterion for sequences of operators
We show that under no hypotheses on the density of the ranges of the mappings involved, an almost-commuting sequence (Tₙ) of operators on an F-space X satisfies the Hypercyclicity Criterion if and only if it has a hereditarily hypercyclic subsequence , and if and only if the sequence (Tₙ ⊕ Tₙ) is hypercyclic on X × X. This strengthens and extends a recent result due to Bès and Peris. We also find a new characterization of the Hypercyclicity Criterion in terms of a condition introduced by Godefroy...
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...