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Distinguishedness of weighted Fréchet spaces of continuous functions

Published online by Cambridge University Press:  20 January 2009

Françoise Bastin
Françoise Bastin
Affiliation:
Université de LiègeInstitut de MathématiqueAvenue des Tilleuls, 154000 Liege, Belgium
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Abstract

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In this paper, we prove that if is an increasing sequence of strictly positive and continuous functions on a locally compact Hausdorff space X such that then the Fréchet space C(X) is distinguished if and only if it satisfies Heinrich's density condition, or equivalently, if and only if the sequence satisfies condition (H) (cf. e.g.‵[1] for the introduction of (H)). As a consequence, the bidual λ∞(A) of the distinguished Köthe echelon space λ0(A) is distinguished if and only if the space λ1(A) is distinguished. This gives counterexamples to a problem of Grothendieck in the context of Köthe echelon spaces.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 2 , June 1992 , pp. 271 - 283
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

REFERENCES

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