Spaces of operators between Fréchet spaces

Source abstract

Abstract Motivated by recent results on the space of compact operators between Banach spaces and by extensions of the Josefson–Nissenzweig theorem to Fréchet spaces, we investigate pairs of Fréchet spaces ( E , F ) such that every continuous linear map from E into F is Montel, i.e. it maps bounded subsets of E into relatively compact subsets of F . As a consequence of our results we characterize pairs of Köthe echelon spaces ( E , F ) such that the space of Montel operators from E into F is complemented in the space of all continuous linear maps from E into F .