Vol. 26, No. 3, 1968

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An L1 algebra for linearly quasi-ordered compact semigroups

Neal Jules Rothman

Vol. 26 (1968), No. 3, 579–588

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
Received: 11 August 1967
Published: 1 September 1968
Neal Jules Rothman