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Two problems of Valdivia on distinguished Fréchet spaces. (English) Zbl 0799.46003

Summary: We construct the following spaces:
(a) a Fréchet space \(E\) with basis which is non-distinguished and has no subspace isomorphic to \(\ell_ 1\);
(b) a non-distinguished Fréchet space \(F\) such that every separable subspace of \(F\) is distinguished (even more, every separable subspace of \(F\) has a separable dual).
These examples answer in the negative two questions posed by Valdivia.

MSC:

46A04 Locally convex Fréchet spaces and (DF)-spaces
46A35 Summability and bases in topological vector spaces
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References:

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