An L¹ algebra for linearly quasi-ordered compact semigroups

Neal Jules Rothman

Vol. 26 (1968), No. 3, 579–588

DOI: 10.2140/pjm.1968.26.579

Abstract

This paper is concerned with obtaining an L¹ algebra for compact commutative linearly quasi-ordered topological semigroups. It will be shown that there is a suitable measure on such a semigroup so that the maximal ideal space of the L¹ algebra with respect to this measure and the bounded measurable semicharacters modulo equal almost everywhere can be identified. It is also proved that the condition x² = y² = xy implies x = y is necessary and sufficient that the L¹ algebra be semisimple.

Mathematical Subject Classification

Primary: 22.05

Milestones

Received: 11 August 1967

Published: 1 September 1968