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Weak containment and Clifford semigroups*

Published online by Cambridge University Press:  14 November 2011

Alan L. T. Paterson
Alan L. T. Paterson
Affiliation:
Department of Mathematics, University of Aberdeen
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Synopsis

Let S be a Clifford semigroup with identity. The weak containment question is posed for S, and answered affirmatively when each of the maximal groups Se in S is amenable. The amenability of S itself is characterised in terms of PL(S), the set of normalised positive definite functions on S arising from the left regular representation of S. A type of mean associated with PL(S) and satisfying a condition weaker than left invariance is introduced.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 81 , Issue 1-2 , 1978 , pp. 23 - 30
Copyright
Copyright © Royal Society of Edinburgh 1978

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