The spine of a Fourier-Stieltjes algebra: corrigenda
Some unfortunate errors from our paper math/0505591 are corrected.
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arXiv subjects
Monica Ilie
Publications and source records attributed to Monica Ilie.
The spine of a Fourier-Stieltjes algebra
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.
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The algebra generated by idempotents in a Fourier-Stieltjes algebra
We study the closed algebra B_I(G) generated by the idempotents in the Fourier-Stieltjes algebra of a locally compact group G. We show that it is a regular Banach algebra with computable spectrum G^I, which we call the idempotent compactification of G. For any locally compact groups G and H, we show that B_I(G) is completely isometrically isomorphic to B_I(H) exactly when G/G_e= H/H_e, where G_e and H_e are the connected components of the identities. We compute some examples to illustrate out results.
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