The spine of a Fourier-Stieltjes algebra
Abstract
We define the spine A*(G) of the Fourier-Stieltjes algebra B(G) of a locally compact group G. A*(G) is graded over a certain semi-lattice, that of non-quotient locally precompact topologies on G. We compute the spine's spectrum G*, which admits a semi-group structure. We discuss homomorphisms from A*(G) to B(H) where H is another locally compact group; and we show that A*(G) contains the image of every completely bounded homomorphism from the Fourier algebra A(H) of any amenable group H. We also show that A*(G) contains all of the idempotents in B(G). Finally, we compute examples for vector groups, abelian lattices, minimally almost periodic groups and the ax+b-group; and we explore the complexity of A*(G) for the discrete rational numbers and free groups.
Keywords
Cite
@article{arxiv.math/0505591,
title = {The spine of a Fourier-Stieltjes algebra},
author = {Monica Ilie and Nico Spronk},
journal= {arXiv preprint arXiv:math/0505591},
year = {2008}
}
Comments
33 pages, a few typos corrected