The algebra generated by idempotents in a Fourier-Stieltjes algebra

摘要

We study the closed algebra B_I(G) generated by the idempotents in theFourier-Stieltjes algebra of a locally compact group G. We show that it is aregular Banach algebra with computable spectrum G^I, which we call theidempotent compactification of G. For any locally compact groups G and H, weshow that B_I(G) is completely isometrically isomorphic to B_I(H) exactly whenG/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.