Uniformly and locally convex asymmetric spaces

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...

Locally Uniformly Convex Norms in Banach Spaces and Their Duals

It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm that is itself locally uniformly convex.

Some Uniformly Convex Spaces

size of the éliminants but the size of their largest prime factor which is important, and secondly it is not essential to take the w's in order of magnitude. In answer, it should be pointed out that after one passes the limits of factor tables, it becomes impracticable to deal with the factors of the éliminant rather than the éliminant. Therefore, since the éliminant (in one case at least) appe...

Approximate Convexity and Submonotonicity in Locally Convex Spaces

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...