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Abstract: In this note we study two related questions. (1) For a compact group G, whatare the ranges of the convolution maps on A(GXG) given for u,v in A(G) by $u Xv |-> u*v- ($v-(s)=v(s^{-1})$) and $u X v |-> u*v$? (2) For a locally compactgroup G and a compact subgroup K, what are the amenability properties of theFourier algebra of the coset space A(G-K)? The algebra A(G-K) was defined andstudied by the first named author.In answering the first question, we obtain for compact groups which do notadmit an abelian subgroup of finite index, some new subalgebras of A(G). Usingthose algebras we can find many instances in which A(G-K) fails the mostrudimentary amenability property: operator weak amenability. However, usingdifferent techniques, we show that if the connected component of the identityof G is abelian, then A(G-K) always satisfies the stronger property that it ishyper-Tauberian, which is a concept developed by the second named author. Wealso establish a criterion which characterises operator amenability of A(G-K)for a class of groups which includes the maximally almost periodic groups.



Author: Brian E. Forrest, Ebrahim Samei, Nico Spronk

Source: https://arxiv.org/



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