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Title: Closed subspaces without Schauder bases in non-archimedean Frechet spaces
Authors: Śliwa, Wiesław
Issue Date: Jun-2001
Publisher: Royal Netherlands Academy of Arts and Sciences
Citation: Indag. Mathem., (N.S.), 12(2),261-271.
Abstract: Let E be an infinite-dimensional non-archimedean Frechet space which is not isomorphic to any of the following spaces: $c_0,c_0 x K^N,K^N$. 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 $c_0 x K^N$ has a Schauder basis.
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