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 ....

In this paper we characterize various sorts of boundedness of the free (abelian) topological group F (X) (A(X)) as well as the free locally-convex linear topological space L(X) in terms of properties of a Tychonoff space X. These properties appear to be close to so-called selection principles, which permits us to show, that (it is consistent with ZFC that) the property of Hurewicz (Menger) is l...

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...

This paper provides new versions of the Farkas lemma characterizing those inequalities of the form f(x) ≥ 0 which are consequences of a composite convex inequality (S ◦ g)(x) ≤ 0 on a closed convex subset of a given locally convex topological vector space X, where f is a proper lower semicontinuous convex function defined on X, S is an extended sublinear function, and g is a vector-valued S-con...

A theory of differential calculus for nonlinear maps between general locally convex spaces is developed. All convergence notions are topological, and only familiarity with basic results from point set topology, differential calculus in Banach spaces, and locally convex space theory is assumed. The chain rule for continuous kth order differentiability, smoothness of inverse functions, and functi...

We study weakly compact operators from a C∗-algebra with values in a complete locally convex space. They constitute a natural non-commutative generalization of finitely additive vector measures with values in a locally convex space. Several results of Brooks, Sâıto and Wright are extended to this more general setting. Building on an approach due to Sâıto and Wright, we obtain our theorems on no...