Restrictions of unbounded continuous linear operators on Fréchet spaces (Q1066412)

It is proved that if E is a Fréchet space, F a closed subspace of a Fréchet space \(F_ 1\) which has a basis and admits a continuous norm and \(T: E\to F\) is a continuous unbounded linear operator, then there is an infinite-dimensional closed nuclear subspace G of E which has a basis such that the restriction of T to G is an isomorphism onto T(G). In the proof, a modification of a result of Bessaga, Pelczynski and Rolewicz, which was employed to construct a nuclear subspace of a Fréchet space is used.