Abstract
The diametral dimension of a nuclear Frechet spaceE, which satisfies (DN) and (Ω), is related to power series spaces Λ1(e) and Λ∞(e) for some exponent sequence e. It is proved thatE contains a complemented copy of Λ∞(e) provided the diametral dimensions ofE and Λ∞(e) are equal and e is stable. Assuming Λ1(e) is nuclear, any subspace of Λ1(e) which satisfies (DN), can be imbedded intoE. Applications of these results to spaces of analytic functions are given.
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