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Imbedding of power series spaces and spaces of analytic functions

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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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Authors and Affiliations

  1. Department of Mathematics, Middle East Technical University, 06531, Ankara, Turkey

    A. Aytuna & T. Terzioĝlu

  2. Fachbereich Mathematik, Bergische Universität Gesamthochschule Wuppertal, 5600, Wuppertal 1, FRG

    J. Krone

Authors
  1. A. Aytuna
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  2. J. Krone
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  3. T. Terzioĝlu
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Support of Turkish Scientific and Technical Research Council is gratefully acknowledged.

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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

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