Ross Stokke

Biflatness and Pseudo-Amenability of Segal Algebras

We investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, L1(G), and the Fourier algebra, A(G), of a locally compact group G. Received by the editors January 9, 2008. Published electronically May 20, 2010. The first author’s research was supported by an NSERC Post Doctoral Fellowship. The second author’s research was supported by NSERC under grant no. 312515-05. The third author’s research was supported by NSERC under grant no. 298444-04. AMS subject classification: 43A20, 43A30, 46H25, 46H10, 46H20, 46L07.

Weak*- continuous homomorphisms of Fourier–Stieltjes algebras

For a locally compact group G, let B(G) denote its Fourier�Stieltjes algebra. Any continuous, piecewise affine map a: Y H ? G induces a completely bounded algebra homomorphism ja: B(G) ? B(H) [14, 15] and we prove that ja is w* � w* continuous if and only if a 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.

AMENABILITY OF BANACH AND C*-ALGEBRAS GENERATED BY UNITARY REPRESENTATIONS

We study the amenability of a locally compact group G in relation to the amenability properties of a variety of C*-algebras and (quantized/dual) Banach algebras naturally associated to a unitary representation of G.