On probabilistic normed spaces under .
On problems concerning extension of linear operations on linear spaces
On projection constant problems and the existence of metric projections in normed spaces.
On property in -spaces
On property (β) of Rolewicz in Musielak-Orlicz sequence spaces equipped with the Orlicz norm
We prove that the Musielak-Orlicz sequence space with the Orlicz norm has property (β) iff it is reflexive. It is a generalization and essential extension of the respective results from [3] and [5]. Moreover, taking an arbitrary Musielak-Orlicz function instead of an N-function we develop new methods and techniques of proof and we consider a wider class of spaces than in [3] and [5].
On pseudonormability of some particular classes of spaces
On p-summable sequences in locally convex spaces.
On Pták's Generalization of the Open-Mapping and Closed-Graph Theorems.
On quasi almost lacunary strong convergence difference sequence spaces defined by a sequence of moduli
On Quasibarrelled Spaces.
On quasi-completeness and sequential completeness in locally convex spaces.
On -reflexive Banach spaces
A Banach space is called -reflexive if for any cover of by weakly open sets there is a finite subfamily covering some ball of radius 1 centered at a point with . We prove that an infinite-dimensional separable Banach space is -reflexive (-reflexive for some ) if and only if each -net for has an accumulation point (resp., contains a non-trivial convergent sequence) in the weak topology of . We show that the quasireflexive James space is -reflexive for no . We do not know...
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