2023/02/19 by M. Anoussis, Anoussis, M., G. K. Eleftherakis +3
Mathematics · #43A20 #43A22 #43A30 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2302.09573
openalex publication_date 2023/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate conditions for the extendibility of continuous algebra homomorphisms ϕ from the Fourier algebra A(F) of a locally compact group F to the Fourier-Stieltjes algebra B(G) of a locally compact group G to maps between the corresponding L^∞ algebras which are weak* continuous. When ϕ is completely bounded and F is amenable, it is induced by a piecewise affine map α: Y→ F where Y⊆ G. We show that extendibility of ϕ is equivalent to α being an open map. We also study the dual problem for contractive homomorphisms ϕ: L1(F)→ M(G). We show that ϕ induces a w* continuous homomorphism between the von Neumann algebras of the groups if and only if the naturally associated map θ (Greenleaf [1965], Stokke [2011]) is a proper map.