Spaces of operators between Fréchet spaces

Abstract

AbstractMotivated 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 fromEintoFis Montel, i.e. it maps bounded subsets ofEinto relatively compact subsets ofF. As a consequence of our results we characterize pairs of Köthe echelon spaces (E,F) such that the space of Montel operators fromEintoFis complemented in the space of all continuous linear maps fromEintoF.