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VECTOR MEASURES OF BOUNDED SEMIVARIATION AND ASSOCIATED CONVOLUTION OPERATORS

Published online by Cambridge University Press:  08 December 2010

PAULETTE SAAB  and
MANGATIANA A. ROBDERA
PAULETTE SAAB
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211, USA email: saabp@missouri.edu
MANGATIANA A. ROBDERA
Affiliation:
Department of Mathematics, University of Botswana, Gaborone, Botswana email: robdera@yahoo.com
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Abstract

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Let G be a compact metrizable abelian group, and let X be a Banach space. We characterize convolution operators associated with a regular Borel X-valued measure of bounded semivariation that are compact (resp; weakly compact) from L1(G), the space of integrable functions on G into L1(G) X, the injective tensor product of L1(G) and X. Along the way we prove a Fourier Convergence theorem for vector measures of relatively compact range that are absolutely continuous with respect to the Haar measure.

Keywords

46G1046B99
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 2 , May 2011 , pp. 333 - 340
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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