On non locally p-convex spaces

On p - Summable Sequences in Locally Convex Spaces †

We follow the notation of [7,10]. In particular, if E[τ ] is a locally convex space (in short l.c.s.), σ(E, E∗), μ(E,E∗) and β(E,E∗) will denote, respectively, the weak, Mackey and strong topology corresponding to the dual pair 〈E, E∗〉. If U is a neighbourhood of 0 in E[τ ], EU denotes the Banach space associated to U and φU : E → EU denotes the corresponding quotient map. Definition 1. Let E[τ...

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.