The algebra generated by idempotents in a Fourier-Stieltjes algebra

Details The algebra generated by idempotents in a Fourier-Stieltjes algebra The algebra generated by idempotents in a Fourier-Stieltjes algebra

2005-10-24

arxiv.org/abs/math/0510514v1

Houston J. Math. 33 (2007), no. 4, 1131--1145.

Mathematics

Functional Analysis

13 pages

Scientific paper

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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