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Isomorphisms between spaces of vector-valued continuous functions

Published online by Cambridge University Press:  20 January 2009

N. J. Kalton
N. J. Kalton
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211
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A theorem due to Milutin [12] (see also [13]) asserts that for any two uncountable compact metric spaces Ω1 and Ω2 the spaces of continuous real-valued functions C(Ω1) and C(Ω2) are linearly isomorphic. It immediately follows from consideration of tensor products that if X is any Banach space then C(Ω1;X) and C(Ω2;X) are isomorphic.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 26 , Issue 1 , February 1983 , pp. 29 - 48
Copyright
Copyright © Edinburgh Mathematical Society 1983

References

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