Spaces of Operators Between Frechet Spaces

Motivated by recent results on the space of compact operators between Banach spaces and by extensions of the Josefson-Nissenzweig theorem to Frechet spaces, we investigate pairs of Frechet 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 Kothe 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.