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Duality properties of spaces of non-Archimedean valued functions

Published online by Cambridge University Press:  09 April 2009

W. Govaerts
W. Govaerts
Affiliation:
Seminarie voor hogere analyse, Galglaan 2, B-9000 Gent, Belgium
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Abstract

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Let C(X, F) be the space of all continuous functions from the ultraregular compact Hausdorff space X into the separated locally K-convex space F; K is a complete, but not necessarily spherically complete, non-Archimedean valued field and C(X, F) is provided with the topology of uniform convergence on X We prove that C(X, F) is K-barrelled (respectively K-quasibarrelled) if and only if F is K-barrelled (respectively K-quasibarrelled) This is not true in the case of R or C-valued functions. No complete characterization of the K-bornological space C(X, F) is obtained, but our results are, nevertheless, slightly better than the Archimedean ones. Finally, we introduce a notion of K-ultrabornological spaces for K non-spherically complete and use it to study K-ultrabornological spaces C(X, F).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 1 , February 1987 , pp. 48 - 56
Copyright
Copyright © Australian Mathematical Society 1987

References

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