Glasgow Mathematical Journal

Research Article

VECTOR MEASURES OF BOUNDED SEMIVARIATION AND ASSOCIATED CONVOLUTION OPERATORS

PAULETTE SAABa1 and MANGATIANA A. ROBDERAa2

a1 Department of Mathematics, University of Missouri, Columbia, Missouri 65211, USA email: saabp@missouri.edu

a2 Department of Mathematics, University of Botswana, Gaborone, Botswana email: robdera@yahoo.com

Abstract

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.

(Received January 27 2010)

(Accepted August 09 2010)

(Online publication December 08 2010)

2010 Mathematics Subject Classification

  • 46G10;
  • 46B99