On some properties of the Banach algebras 𝐴_{𝑝}(𝐺) for locally compact groups

Granirer, Edmond E.

doi:10.1090/S0002-9939-1985-0806074-X

On some properties of the Banach algebras $A_ p(G)$ for locally compact groups
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Proc. Amer. Math. Soc. 95 (1985), 375-381 Request permission

Abstract:

We strengthen and improve theorems of Choquet-Deny and of Foguel concerning convolution equations and iterates of convolution of a measure to all algebras ${A_p}(G)$ and all locally compact groups. Furthermore, we improve results of H. P. Rosenthal on ideals of $A(G)$ to the algebras ${A_p}(G)$ and show that some hold for amenable groups but not for free nonabelian groups. Finally, we improve a (possibly) weak version of a theorem of Gilbert on projections onto some subspaces of ${L^\infty }(G)$ to all locally compact groups.

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