On random variables having values in a vector lattice
On reducibility of some operator semigroups and algebras on locally convex spaces.
On regularity of inductive limits
On relatively disjoint families of measures, with some applications to Banach space theory
On Riesz homomorphisms in unital -algebras
The main topic of the first section of this paper is the following theorem: let be an Archimedean -algebra with unit element , and a Riesz homomorphism such that for all . Then every Riesz homomorphism extension of from the Dedekind completion of into itself satisfies for all . In the second section this result is applied in several directions. As a first application it is applied to show a result about extensions of positive projections to the Dedekind completion. A second application...
On Riesz homomorphisms in von Neumann regular f-algebra.
On Schwartz groups
We introduce a notion of a Schwartz group, which turns out to be coherent with the well known concept of a Schwartz topological vector space. We establish several basic properties of Schwartz groups and show that free topological Abelian groups, as well as free locally convex spaces, over hemicompact k-spaces are Schwartz groups. We also prove that every hemicompact k-space topological group, in particular the Pontryagin dual of a metrizable topological group, is a Schwartz group.
On Schwartz Spaces and Mackey Convergence
On Sectionally Dense Summability Fields.
On semi-inner product spaces, II
On separable Banach spaces containing all separable reflexive Banach spaces
On separation theorems for subadditive and superadditive functionals
We generalize the well known separation theorems for subadditive and superadditive functionals to some classes of not necessarily Abelian semigroups. We also consider the problem of supporting subadditive functionals by additive ones in the not necessarily commutative case. Our results are motivated by similar extensions of the Hyers stability theorem for the Cauchy functional equation. In this context the so-called weakly commutative and amenable semigroups appear naturally. The relations between...
On sequences in vector lattices
In this paper we investigate conditions for a system of sequences of elements of a vector lattice; analogous conditions for systems of sequences of reals were studied by D. E. Peek.
On sequential convergence in weakly compact subsets of Banach spaces
We construct an example of a Banach space E such that every weakly compact subset of E is bisequential and E contains a weakly compact subset which cannot be embedded in a Hilbert space equipped with the weak topology. This answers a question of Nyikos.
On sequentially retractive inductive limits.
On Simons' version of Hahn-Banach-Lagrange theorem
In this paper we generalize in Theorem 12 some version of Hahn-Banach Theorem which was obtained by Simons. We also present short proofs of Mazur and Mazur-Orlicz Theorem (Theorems 2 and 3).
On some aspects of Jensen-Menger convexity.
The paper contains various results concerning the so-called homogeneity sets for convex functions defined on convex subsets of some special metric spaces named G-space (cf. H. Busemann [1]). A closed graph theorem for such type mappings is also presented.
On some BK spaces.
On some classes of function sequence spaces
On some classes of linear function transformations of sequences (III)