On Sectionally Dense Summability Fields.
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...
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.
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.
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).
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.
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.