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Operator Segal algebras in Fourier algebras

Brian E. ForrestNico SpronkPeter J. Wood — 2007

Studia Mathematica

Let G be a locally compact group, A(G) its Fourier algebra and L¹(G) the space of Haar integrable functions on G. We study the Segal algebra S¹A(G) = A(G) ∩ L¹(G) in A(G). It admits an operator space structure which makes it a completely contractive Banach algebra. We compute the dual space of S¹A(G). We use it to show that the restriction operator u u | H : S ¹ A ( G ) A ( H ) , for some non-open closed subgroups H, is a surjective complete quotient map. We also show that if N is a non-compact closed subgroup, then the averaging...

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