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Contractive homomorphisms of the Fourier algebras
Author(s) -
Le Pham Hung
Publication year - 2010
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdq048
Subject(s) - homomorphism , mathematics , algebra homomorphism , locally compact group , algebra over a field , fourier transform , pure mathematics , combinatorics , discrete mathematics , locally compact space , mathematical analysis
Let G and H be locally compact groups. We prove that, for every contractive homomorphism θ from A( G ), the Fourier algebra of G , into B( H ), the Fourier–Stieltjes algebra of H , there exist a continuous group homomorphism or anti‐homomorphism τ from an open subgroup Ω of H into G and elements u 0 ∈ G , r 0 ∈ H such that θ ( f ) ( t ) = {f ( u 0 τ ( r 0 τ ) )if t ∊ r 0 − 1 Ω ,0if t ∊ H \ r 0 − 1 Ω .We also characterize positive homomorphisms from A( G ) into B( H ) and contractive isomorphisms from B( G ) onto B( H ).