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Rosenthal 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 metrizable group and Λ a subset of Ĝ, the dual group of G. If X has the Radon-Nikodym property and is separable then has the Radon-Nikodym property. One consequence of this is that CΛ(G, X) has the Radon-Nikodym property whenever X has the Radon-Nikodym property and the Schur property and Λ is a Rosenthal set. A partial stability property for products of Rosenthal sets is also obtained.

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 54 , Issue 2 , April 1993 , pp. 213 - 220
Copyright
Copyright © Australian Mathematical Society 1993

References

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