The Lagrange multipliers theorem for locally convex metric spaces

Egoroff Theorem for Operator-Valued Measures in Locally Convex Cones

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

Riesz Type Theorem in Locally Convex Spaces

The present paper is concerned with some representatons of linear mappings of continuous functions into locally convex vector spaces, namely Theorem. If X is a complete Hausdorff locally convex vector space, then a general form of weakly compact mapping T : C[a, b] → X is of the form Tg = ∫ b a g(t)dx(t), where the function x(·) : [a, b] → X has a weakly compact semivariation on [a, b]. This th...

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.

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