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7.—Convolution of Vector Measures*

Published online by Cambridge University Press:  14 February 2012

A. J. White
A. J. White
Affiliation:
Department of Mathematics, University of Aberdeen
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Synopsis

In this paper we consider the problem of defining a convolution, analogous to the classical convolution of scalar measures, of measures defined on the Borel sets of a locally compact semi-group S and having values in a Banach algebra . Using the bilinearintegral introduced by Bartle we show that the formalism of the scalar case persists in situations of considerable generality so that the formula

suitably interpreted, gives a Banach algebra structure to a large class of valued measures defined on S. Themethods exploit the connection between vector measures and operators and involve some results of independent interest.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 73 , 1975 , pp. 117 - 135
Copyright
Copyright © Royal Society of Edinburgh 1975

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