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Closed subspaces without Schauder bases in non-archimedean Fréchet spaces

Authors
Journal
Indagationes Mathematicae
0019-3577
Publisher
Elsevier
Publication Date
Volume
12
Issue
2
Identifiers
DOI: 10.1016/s0019-3577(01)80031-8

Abstract

Abstract Let E be an infinite-dimensional non-archimedean Fréchet space which is not isomorphic to any of the following spaces: c 0, c 0 × K N , K N . It is proved that E contains a closed subspace without a Schauder basis (even without a strongly finite-dimensional Schauder decomposition). Conversely, it is shown that any closed subspace of c 0 × K N has a Schauder basis.

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