IMCS/Publications/BASM/Issues/BASM n.3 (37), 2001/

On weighted functional spaces.

Authors: Ipate D.M.


All spaces under consideration are Tychonoff. Let E be a locally convex vector space. Every Nachbin set V of weights on a space X generates the weighted space CV(X, E) and its subspace CV(X, E) of mappings from CV(X, E) vanishing at infinity. Topological properties of this spaces and of continuous linear mappings φ:CV(X, T)→E are studied. Some approximation theorems of Stone-Weierstrass type and of Diedone type are proved. The present paper is connected with the results of Nachbin [5, 6], Abel [1], Păltineanu [9], Choban [2], Choban and Ipate [3], Valov [9]. We shall use the notations and terminology from [4, 8].