Granirer, Edmond E. On some properties of the Banach algebras \(A_ p(G)\) for locally compact groups. (English) Zbl 0599.43005 Proc. Am. Math. Soc. 95, 375-381 (1985). Let G be a locally compact group. For any function h on G define \(h^ v\) by \(h^ v(x)=h(x^{-1})\). For \(1\leq p\leq \infty\) let \(A_ p(G)=\{\sum^{\infty}_{1}f_ n*g^ v_ n |\) \(f_ n\in L^ q\), \(g_ n\in L^ p\), \(\sum^{\infty}_{1}\| f_ n\|_ q \| g_ n\|_ p<\infty \}\) where q is the conjugate index of p. Under pointwise operations \(A_ p(G)\) is an algebra (in the case \(p=2\) called the Fourier algebra of G). The author shows that a theorem of S. Foguel and a theorem of G. Choquet and J. Deny concerning measures on abelian groups are very special cases of theorems on multipliers of \(A_ p(G)\). He also extends two results of H. P. Rosenthal on ideals of the Fourier algebra of an abelian group and proves a theorem on existence of projections related to a theorem of J. E. Gilbert. Reviewer: M.Leinert Cited in 1 ReviewCited in 13 Documents MSC: 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc. Keywords:generalized Fourier algebra; locally compact group; multipliers; existence of projections PDFBibTeX XMLCite \textit{E. E. Granirer}, Proc. Am. Math. Soc. 95, 375--381 (1985; Zbl 0599.43005) Full Text: DOI