Enriched locally convex structures, differential calculus and Riesz representation

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...

Computable Riesz Representation for Locally Compact Hausdorff Spaces

By the Riesz Representation Theorem for locally compact Hausdorff spaces, for every positive linear functional I on K(X) there is a measure μ such that I(f) = R f dμ, where K(X) is the set of continuous real functions with compact support on the locally compact Hausdorff space X. In this article we prove a uniformly computable version of this theorem for computably locally compact computable Ha...

The Riesz representation theorem

Differential forms on locally convex spaces and the Stokes formula

We prove a version of the Stokes formula for differential forms on locally convex spaces announced in [10]. The main tool used for proving this formula is the surface layer theorem proved in the paper [6] by the author. Moreover, for differential forms of a Sobolev-type class relative to a differentiable measure [1], we compute the operator adjoint to the exterior differential in terms of stand...

Approximate Convexity and Submonotonicity in Locally Convex Spaces