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Nuclear Fréchet spaces with locally round finite dimensional decompositions

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Abstract

A class of finite dimensional decompositions (FDDs), called locally round, is introduced in Fréchet spaces. A Fréchet space with a locally round FDD can be viewed as a generalization of a Köthe space. The block subspaces and block quotients of such a space are always complemented and have a basis. Conversely, sometimes these properties characterize an FDD being locally round.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Clarkson College of Technology, 13676, Potsdam, NY, U.S.A.

    Ed Dubinsky

  2. Department of Mathematics, University of Helsinki, Hallituskatu 15, SF-00100, Helsinki 10, Finland

    Lasse Holmström

Authors
  1. Ed Dubinsky
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  2. Lasse Holmström
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Dubinsky, E., Holmström, L. Nuclear Fréchet spaces with locally round finite dimensional decompositions. Monatshefte für Mathematik 97, 257–275 (1984). https://doi.org/10.1007/BF02349625

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  • DOI: https://doi.org/10.1007/BF02349625

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