Approximation Results in the Strict Topology

Stone-weierstrass Theorems for the Strict Topology

1. Let X be a locally compact Hausdorff space, E a (real) locally convex, complete, linear topological space, and (C*(X, E), ß) the locally convex linear space of all bounded continuous functions on X to E topologized with the strict topology ß. When E is the real numbers we denote C*(X, E) by C*(X) as usual. When E is not the real numbers, C*(X, E) is not in general an algebra, but it is a mod...

The Strict Topology and Compactness in the Space of Measures

The strict topology j3 on the space C(S) of bounded complex valued continuous functions on a locally compact space 5 was introduced by R. C. Buck [ l ] and has been studied by Glicksberg [4] and Wells [9], Among the problems in mathematics which have seen successful applications of the strict topology are various ones in spectral synthesis (Herz [6]) and spaces of bounded analytic functions (Sh...

Some Results on p-Best Approximation in Vector Spaces

Bishop's Generalized Stone-weierstrass Theorem for the Strict Topology

1. Let X be a locally compact Hausdorff space, C(X)ß the locally convex topological vector space obtained from all bounded complex continuous functions on X by employing the strict topology [2]. The present note is devoted to a version of Bishop's generalized StoneWeierstrass theorem [l] applicable to certain subspaces of C(X)ß-, essentially it is a footnote to an earlier paper [4], in which a ...

Comparison Results without Strict Convexity

In this paper we establish a comparison result for solutions to the problem minimize ∫ Ω l(‖∇u(x)‖) dx or to the problem minimize ∫ Ω l(γC(∇u(x)) dx, for a special class of solutions, without assuming neither smoothness nor strict convexity of l.