We provide necessary and/or sufficient conditions on vector spaces V of real sequences to be a Fréchet space such that each coordinate map is continuous, is, locally convex FK space. In particular, we show if c00(I)?V???(I) for some ideal I ?, then and only there exists an infinite set S?? which every subset does not belong I.

A theorem due to Milutin [12] (see also [13]) asserts that for any two uncountable compact metric spaces Qt and Q2> t n e spaces of continuous real-valued functions C ^ ) and C(Q2) are linearly isomorphic. It immediately follows from consideration of tensor products that if X is any Banach space then QQ^X) and C(Q2;X) are isomorphic. The purpose of this paper is to show that this conclusion is ...