Abstract
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.
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Aytuna, A., Krone, J. & Terzioĝlu, T. Imbedding of power series spaces and spaces of analytic functions. Manuscripta Math 67, 125–142 (1990). https://doi.org/10.1007/BF02568426
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DOI: https://doi.org/10.1007/BF02568426