Arens regularity of \(A_\Phi (G)\) (Q6561677)

Let \(G\) be a locally compact group and \(\Phi\) be a Young function. The authors study Arens regularity of the Orlicz space \(L^\Phi(G)\) versions of the Figà-Talamanca Herz algebra \(A_\Phi(G)\). They show that if the algebra \(A_\Phi(G)\) is Arens regular then \(G\) is discrete. Further, for an amenable group \(G\), they show that \(A_\Phi(G)\) is reflexive if and only if \(G\) is finite under some assumptions on \(\Phi\).