Locally convex spaces with fundamental sequences

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...

Asymmetric locally convex spaces

The aim of the present paper is to introduce the asymmetric locally convex spaces and to prove some basic properties. Among these I do mention the analogs of the EidelheitTuckey separation theorems, of the Alaoglu-Bourbaki theorem on the weak compactness of the polar of a neighborhood of 0, and a Krein-Milman-type theorem. These results extend those obtained by Garcı́a-Raffi et al. (2003) and Co...

Approximate Convexity and Submonotonicity in Locally Convex Spaces

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.

Seminorms and Locally Convex Spaces

The first point is to describe vector spaces with topologies arising from (separating) families of semi-norms. These all turn out to be locally convex, for straightforward reasons. The second point is to check that any locally convex topological vectorspace's topology can be given by a collection of seminorms. These seminorms are made in a natural way from a local basis consisting of balanced c...