Nuclear topologies on non-archimedean locally convex spaces

Non–archimedean Sequential Spaces and the Finest Locally Convex Topology with the Same Compactoid Sets

For a non-Archimedean locally convex space (E, τ), the finest locally convex topology having the same as τ convergent sequences and the finest locally convex topology having the same as τ compactoid sets are studied.

Harmonic functions in non-locally convex spaces

Banach Envelopes of Non-locally Convex Spaces

Then Xc is the completion of {X, \\ \\c). Alternatively || ||c is the Minkowski functional of the convex hull of the unit ball. Xc has the property that any bounded linear operator L:X —> Z into a Banach space extends with preservation of norm to an operator L\XC —» Z. The Banach envelope of / (0 < p < 1) is, of course, lx. In 1969, Duren, Romberg and Shields [3] identified the dual space of H_...

On the dual of certain locally convex function spaces

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.

Order continuous linear functionals on non-locally convex Orlicz spaces

The space of all order continuous linear functionals on an Orlicz space L defined by an arbitrary (not necessarily convex) Orlicz function φ is described.