"A Representation Theorem for D-Rings" by Karim Boulabiar
 

Document Type

Lecture

Publication Date

3-3-2003

Abstract

Let ��(��) be the space of all real-valued functions on a completely regular topological space ��, and let *be an associative multiplication in ��(��). Then ��(��) is a D-ring with respect to * if and only if * is a weighted composition multiplication in ��(��). The latter means that there exists a weight function �� in ��(��) and two maps �� and �� from �� into �� such that (�� * ��)(��) = ��(��)��(��(��))��(��(��)) for all �� in �� and ��, �� in ��(��).

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