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Weak*- continuous homomorphisms of Fourier–Stieltjes algebras

Published online by Cambridge University Press:  01 July 2008

MONICA ILIE  and
ROSS STOKKE
MONICA ILIE
Affiliation:
Department of Mathematical Sciences, Lakehead University, Thunder Bay, ON, Canada, P7B 5E1. e-mail: milie@lakeheadu.ca
ROSS STOKKE
Affiliation:
Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, Canada, R3B 2E9. e-mail: r.stokke@uwinnipeg.ca
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Abstract

For a locally compact group G, let B(G) denote its Fourier–Stieltjes algebra. Any continuous, piecewise affine map α: Y ⊂ H → G induces a completely bounded algebra homomorphism jα: B(G) → B(H) [14, 15] and we prove that jα is w* – w* continuous if and only if α is an open map. This extends one of the main results in [3], due to M.B. Bekka, E. Kaniuth, A.T. Lau and G. Schlichting. Several classical theorems regarding isomorphisms and extensions of homomorphisms on group algebras of abelian groups are extended to the setting of Fourier–Stieltjes algebras of amenable groups. As applications, when G is amenable we provide complete characterizations of those maps between Fourier–Stieltjes algebras that are either associated to a piecewise affine mapping, or are completely bounded and w* – w* continuous.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 1 , July 2008 , pp. 107 - 120
Copyright
Copyright © Cambridge Philosophical Society 2008

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