Imbedding of power series spaces and spaces of analytic functions

The diametral dimension of a nuclear Fréchet spaceE, which satisfies (DN) and (Ω), is related to power series spaces Λ₁(ε) and Λ_∞(ε) for some exponent sequence ε. It is proved thatE contains a complemented copy of Λ_∞(ε) provided the diametral dimensions ofE and Λ_∞(ε) are equal and ε is stable. Assuming Λ₁(ε) is nuclear, any subspace of Λ₁(ε) which satisfies (DN), can be imbedded intoE. Applications of these results to spaces of analytic functions are given. Support of Turkish Scientific and Technical Research Council is gratefully acknowledged.