Special uniform approximations of continuous vector-valued functions. II: Special approximations in \(C_{X}(T)\otimes C_{Y}(S)\).
Continuing his previous investigations [see J. Approximation Theory 119, No. 2, 291--299 (2002; Zbl 1023.46008)], the author defines and studies a new kind of approximation, called special uniform approximation, for functions in the spaces \(\,C_{X\otimes Y}(T\times S)\,\) and \(\, C_ \infty(T\times S,X\otimes Y)\,\) by elements in the tensor products \(C_ X(T)\otimes C_ Y(S)\,\) and \(C_ 0(T,X)\otimes C_ 0(S,Y),\, \) respectively. Here \(T,S\) are Hausdorff topological spaces and \(X,Y\) Hausdorff locally convex spaces over \(\mathbb R\) or \(\mathbb C\). As corollary he obtains, among other results, the density of \(C_ 0(T,X)\otimes C_ 0(S,Y),\, \) in \(C_ 0(T\times S,X\otimes Y)\) with respect to the inductive limit topology.
scientific article; zbMATH DE number 1970541