Description:
<jats:title>Abstract</jats:title><jats:p>In this article we continue the study of weighted inductive limits of spaces of Fréchet-valued continuous functions, concentrating on the problem of projective descriptions and the barrelledness of the corresponding “projective hull”. Our study is related to the work of Vogt on the study of pairs (<jats:italic>E, F</jats:italic>) of Fréchet spaces such that every continuous linear mapping from <jats:italic>E</jats:italic> into <jats:italic>F</jats:italic> is bounded and on the study of the functor Ext<jats:sup>1</jats:sup> (<jats:italic>E, F</jats:italic>) for pairs (<jats:italic>E, F</jats:italic>) of Fréchet spaces.</jats:p>