Sequence space representations of the spaces DL1,(ω)(RN) and of its dual D'L1,(ω)(RN), the space of bounded ultradistributions of Beurling type, are presented, in case the weight ω is a strong weight.
Let be an Archimedean Riesz space with a weak order unit . A sufficient condition under which Dedekind [-]completeness of the principal ideal can be lifted to is given (Lemma). This yields a concise proof of two theorems of Luxemburg and Zaanen concerning projection properties of -spaces. Similar results are obtained for the Riesz spaces , , of all functions of the th Baire class on a metric space .
A simple proof is given of a Monge-Kantorovich duality theorem for a lower bounded lower semicontinuous cost function on the product of two completely regular spaces. The proof uses only the Hahn-Banach theorem and some properties of Radon measures, and allows the case of a bounded continuous cost function on a product of completely regular spaces to be treated directly, without the need to consider intermediate cases. Duality for a semicontinuous cost function is then deduced via the use of an...
The splitting problem is studied for short exact sequences consisting of countable projective limits of DFN-spaces (*) 0 → F → X → G → 0, where F or G are isomorphic to the space of distributions D'. It is proved that every sequence (*) splits for F ≃ D' iff G is a subspace of D' and that, for ultrabornological F, every sequence (*) splits for G ≃ D' iff F is a quotient of D'