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Operator Segal algebras in Fourier algebras
Let $G$ be a locally compact group, $\mathrm{A}(G)$ its Fourier algebra and $\mathrm{L}^1(G)$ the space of Haar integrable functions on $G$. We study the Segal algebra ${\mathrm{S}^1\!\mathrm{A}(G)}= {\mathrm{A}(G)}\cap{\rm L}^1(G)$ in ${\mathrm{A}(G)}$.