Isomorphisms of the Fourier algebras in crossed products

Yoshikazu Katayama

Vol. 86 (1980), No. 2, 505–511

DOI: 10.2140/pjm.1980.86.505

Abstract

Let (M,G,α), (N,H,β) be W^∗-systems, F_α(G;M_∗) and F_β(H;N_∗), their Fourier algebras. The main result is that F_α(G;M_∗) and F_β(H;N_∗) are isometrically isomorphic as Banach algebras if and only if M (resp. G) is isomorphic to N (resp. H) by 𝜃 (resp. I) such that β_I(g) ∘ 𝜃 = 𝜃 ∘ α_g for all g ∈ G, or M (resp. G) is anti-isomorphic to N (resp. H) such that β_I(g⁻¹) ∘ 𝜃 = 𝜃 ∘ α_g for all g ∈ G.

Mathematical Subject Classification 2000

Primary: 46L55

Secondary: 22D25, 43A15

Milestones

Received: 30 January 1979

Published: 1 February 1980