Tensor products of Fréchet or (DF)-spaces with a Banach space

Abstract

The aim of the present article is to study the projective tensor product of a Fréchet space and a Banach space and the injective tensor product of a (DF)-space and a Banach space. The main purpose is to analyze the connection of the good behaviour of the bounded subsets of the projective tensor product and of the locally convex structure of the injective tensor product with the local structure of the Banach space.