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Riesz sets and the Radon-Nikodym property

Part of: Abstract harmonic analysis Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  09 April 2009

Patrick N. Dowling
Patrick N. Dowling
Affiliation:
Miami UniversityOxford, Ohio 45056, U.S.A.
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Abstract

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Let X be a complex Banach space, G a compact abelian group and Λ a subset of Ĝ, the dual group pf G. Then LΛ1(G, X) has the Radon-Nikodym property if and only if X has the Radon-Nikodym property and Λ is Riesz set. In particular, H1 (T, X) has the Radon-Nikodym property if and only if X has the Radon-Nikodym property. This solves a problem of Hensgen.

Keywords

Riesz setsRadon-Nikodym Property

MSC classification

Secondary: 46B22: Radon-Nikodým, Kreĭn-Milman and related properties 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 49 , Issue 2 , October 1990 , pp. 303 - 308
Copyright
Copyright © Australian Mathematical Society 1990

References

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