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BANACH SPACES WITH THE RIEMANN–LEBESGUE OR THE ANALYTIC RIEMANN–LEBESGUE PROPERTY

Published online by Cambridge University Press:  24 March 2003

SHANGQUAN BU  and
RALPH CHILL
SHANGQUAN BU
Affiliation:
Department of Mathematical Science, University of Tsinghua, Beijing 100084, Chinasbu@math.tsinghua.edu.cn
RALPH CHILL
Affiliation:
Abteilung Angewandte Analysis, Universität Ulm, 89069 Ulm, Germanychill@mathematik.uni-ulm.de
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Abstract

In this note, two geometric properties of Banach spaces are proposed and discussed, related to the validity of the lemma of Riemann–Lebesgue in spaces of weakly integrable functions. The class of Banach spaces with the analytic Riemann–Lebesgue property is shown to be precisely the class of Banach spaces for which a weak form of a theorem of Ingham holds.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 5 , September 2002 , pp. 569 - 581
Copyright
© The London Mathematical Society 2002

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Footnotes

The first author is supported by the Alexander-von-Humboldt Foundation and the NSF of China. The second author is supported by the Deutscher Akademischer Austauschdienst (Stipendium im Rahmen des gemeinsamen Hochschulsonderprogramms III von Bund und Ländern über den DAAD). This support is gratefully acknowledged.