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Journal of the London Mathematical Society 1993 s2-48(1):152-166; doi:10.1112/jlms/s2-48.1.152
© 1993 by London Mathematical Society
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© Oxford University Press

On the Spectrum of L{infty}(G)

A. T. Lau, A. R. Medghalchi and J. S. Pym

University of Alberta Edmonton Alberta Canada T6G 2G1
Teacher Training University Tehran 49 Mofateh Avenue Tehran Iran
University of Sheffield Sheffield S3 7RH

Received 3 October 1991. Revision received 28 February 1992.

We investigate the algebraic structure of the spectrum {Omega} of L{infty}(G) for a locally compact group G. In contrast to the compact and discrete cases, when G has neither of these properties, {Omega} is never a semigroup. For {sigma}compact G we determine exactly when the product of two elements of {Omega}. is in {Omega}, but we present an example which suggests that for general groups the underlying set theory may have an effect. Our principal tool, which has independent interest, is a topological structure theorem for the LB-compactification of an arbitrary locally compact group.


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