## 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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