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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,gk); and (c) 1 > p > 2 and F is a quotient of a countable product of Lp(μn) spaces. Then, F is Montel if and only if no infinite dimensional subspace of F is normable.
