Certain classes of locally convex space having non complete separated quotients are studied and consequently results about -completeness are obtained. In particular the space of L. Schwartz is not -complete where denotes a non-empty open set of the euclidean space .
∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany).The space K[0, 1] of differences of convex functions on the closed interval [0, 1] is investigated as a dual Banach space. It is proved that a continuous function f on [0, 1] belongs to K[0, 1]
Let G be a locally compact group, let (φ,ψ) be a complementary pair of Young functions, and let and be the corresponding Orlicz spaces. Under some conditions on φ, we will show that for a Banach -submodule X of , the multiplier space is a dual Banach space with predual , where the closure is taken in the dual space of . We also prove that if is a Δ₂-regular N-function, then , the space of convolutors of , is identified with the dual of a Banach algebra of functions on G under pointwise...
Let Ω be an open connected subset of . We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.
We give some new properties of the space and we apply them to the σ-core theory. These results generalize those by Choudhary and Yardimci.