AnL1algebra for linearly quasi-ordered compact semigroups
Neal J. Rothman · Pacific Journal of Mathematics · 1968
This paper is concerned with obtaining an L 1 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 L 1 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 x 2 = y 2 = xy implies x = y is necessary and sufficient that the L 1 algebra be semisimple.