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)
On some classes of linear topological spaces
On some classes of linear topological spaces II
On some convex stes and their exteme points.
On some countably modulared spaces
On some curves in vector lattices.
On some dense subspaces of topological linear spaces
On some difference sequence sets and their topological properties.
On some ergodic properties for continuous and affine functions
Two problems posed by Choquet and Foias are solved:(i) Let be a positive linear operator on the space of continuous real-valued functions on a compact Hausdorff space . It is shown that if converges pointwise to a continuous limit, then the convergence is uniform on .(ii) An example is given of a Choquet simplex and a positive linear operator on the space of continuous affine real-valued functions on , such thatfor each in , but does not converge to 0.