Vol. 86, No. 2, 1980

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ISSN: 0030-8730
Isomorphisms of the Fourier algebras in crossed products

Yoshikazu Katayama

Vol. 86 (1980), No. 2, 505–511
Abstract

Let (M,G,α), (N,H,β) be W-systems, Fα(G;M) and Fβ(H;N), their Fourier algebras. The main result is that Fα(G;M) and Fβ(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 βI(g) 𝜃 = 𝜃 αg for all g G, or M (resp. G) is anti-isomorphic to N (resp. H) such that βI(g1) 𝜃 = 𝜃 αg for all g G.

Mathematical Subject Classification 2000
Primary: 46L55
Secondary: 22D25, 43A15
Milestones
Received: 30 January 1979
Published: 1 February 1980
Authors
Yoshikazu Katayama
Division of Mathematical Sciences
Osaka Kyoiku University
4-698-1 Asahigoka
Kashiwara
Osaka 5828582
Japan