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LOCALLY COMPACT GROUPS, INVARIANT MEANS AND THE CENTRES OF COMPACTIFICATIONS

Published online by Cambridge University Press:  01 August 1997

A. T. LAU ,
P. MILNES  and
J. S. PYM
A. T. LAU
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
P. MILNES
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario N6A 3K7, Canada
J. S. PYM
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH
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Abstract

This paper brings together two apparently unrelated results about locally compact groups G by giving them a common proof. The first concerns the number of topologically left invariant means on L∞(G), while the second states that the topological centre of the largest semigroup compactification of G is simply G itself. On the way, we introduce as vital tools some new compactifications of the half line ([0, ∞), +), we produce a right invariant pseudometric on a compactly generated G for which the bounded sets are precisely the relatively compact sets, and we receive striking confirmation that some algebraic properties of semigroups can be transferred by maps which are quite far from being homomorphisms.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 56 , Issue 1 , August 1997 , pp. 77 - 90
Copyright
The London Mathematical Society 1997

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