Uniform spaces, spanier quasitopologies, and a duality for locally convex algebras

Stable and Total Fenchel Duality for Convex Optimization Problems in Locally Convex Spaces

STABLE AND TOTAL FENCHEL DUALITY FOR CONVEX OPTIMIZATION PROBLEMS IN LOCALLY CONVEX SPACES∗ CHONG LI† , DONGHUI FANG‡ , GENARO LÓPEZ§ , AND MARCO A. LÓPEZ¶ Abstract. We consider the optimization problem (PA) infx∈X{f(x) + g(Ax)} where f and g are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y , respectively, and A is a linear operator from X to Y ....

Approximate Convexity and Submonotonicity in Locally Convex Spaces

Banach Algebras of Operators on Locally Convex 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...

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...