Montel Subspaces in the Countable Projective Limits of L p ( μ )-Spaces

Source abstract

Abstract Let us suppose one of the following conditions: (a) p ≧ 2 and F is a closed subspace of a projective limit (b) p = 1 and F is a complemented subspace of an echelon Köthe space of order 1, Λ (X,β,μ,g k ) ; and (c) 1 > p > 2 and F is a quotient of a countable product of L p ( μ n ) spaces. Then, F is Montel if and only if no infinite dimensional subspace of F is normable.