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manuscripta mathematica

, Volume 5, Issue 2, pp 147–153 | Cite as

Reflexivitât und Schauder Basen vom Typ p und p in Lokalkonvexen Râumen

  • Ulrich Mertins
Article
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Abstract

In the present paper the following theorem is proved: Let E be a barrelled locally convex space with a Schauder base of type P or P. Then E is normable.

In continuation of the investigations of singer [8] and Retherford [5] we obtain by the above result a characterization of the reflexivity of a locally convex space with a base in terms of the behaviour of its subspaces.

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Literatur

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    DUBINSKY, E. and J.R. RETHERFORD: Schauder bases and Köthe sequence spaces. Trans. Amer. Math. Soc. 130 (1968) 265–280Google Scholar
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    RETHERFORD, J.R.: Bases, basic sequences and reflexivity of linear topologtical spaces. Math. Annalen 164 (1966) 280–285Google Scholar
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Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • Ulrich Mertins
    • 1
  1. 1.Mathematisches InstitutUniversität KarlsruheKarlsruhe 1

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