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Order structure on certain classes of ideals in group algebras and amenability

Published online by Cambridge University Press:  17 April 2009

Yuji Takahashi
Yuji Takahashi
Affiliation:
Department of Mathematics, Hokkaido University of Education, Hakodate 040–8567, Japan, e-mail: ytakahas@cc.hokkyodai,ac.jp
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Abstract

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Let G be a separable, locally compact group and let d (G) be the set of all closed left ideals in L1(G) which have the form Jμ = {f − f ∗ μ: f ∈ L1(G)}− for some discrete probability measure μ. It is shown that if d (G) has a unique maximal element with respect to the order structure by set inclusion, then G is amenable. This answers a problem of G.A. Willis. We also examine cardinal numbers of the sets of maximal elements in d (G) for nonamenable groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 1 , August 2002 , pp. 69 - 73
Copyright
Copyright © Australian Mathematical Society 2002

References

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