Convolutions on the Haagerup tensor products of Fourier algebras

2014/06/19 by Mehdi Rostami, M. Rostami, Rostami, Mehdi +2
Mathematics · #43A10 #43A30 #46L07 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:43A10 #msc:43A30 #msc:46L07

paper · pdf · doi:10.48550/arxiv.1406.5133

12 pages

arxiv created 2014/06/19 · openalex publication_date 2014/06/19 · arxiv updated 2014/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the ranges of the maps of convolution u⊗ v↦ u∗ v and a `twisted' convolution u⊗ v↦ u∗ \checkv (\checku(s)=u(s^-1)) and on the Haagerup tensor product of a Fourier algebra of a compact group A(G) with itself. We compare the results to result of factoring these maps through projective and operator projective tensor products. We notice that (A(G),∗) is an operator algebra and observe an unexpected set of spectral synthesis.

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