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RIEMANN–LEBESGUE PROPERTIES OF BANACH SPACES ASSOCIATED WITH SUBSETS OF COUNTABLE DISCRETE ABELIAN GROUPS

Published online by Cambridge University Press:  01 May 2003

PATRICK N. DOWLING  and
NARCISSE RANDRIANANTOANINA
PATRICK N. DOWLING
Affiliation:
Department of Mathematics and Statistics, Miami University, Oxford, OH 45056 e-mail: dowlinpn@muohio.edu, randrin@muohio.edu
NARCISSE RANDRIANANTOANINA
Affiliation:
Department of Mathematics and Statistics, Miami University, Oxford, OH 45056 e-mail: dowlinpn@muohio.edu, randrin@muohio.edu
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Abstract

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For a subset $\Lambda$ of the dual group of a compact metrizable abelian group, we introduce the type I-, II-, and III-$\Lambda$-Riemann–Lebesgue property of a Banach space. As an application we use these properties to characterize Rajchman sets.

Keywords

46B2246S1043A25
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 1 , January 2003 , pp. 159 - 166
Copyright
2003 Glasgow Mathematical Journal Trust