On Musielak-Orlicz spaces isometric to \(L_2\) or \(L \infty\)
It is proved that a Musiełak-Orlicz space \(L_\Phi\) of real valued functions which is isometric to a Hilbert space coincides with \(L_2\) up to a weight, that is \(\Phi(u,t)= c(t)u^2\). Moreover, it is shown that any surjective isometry between \(L_\Phi\) and \(L_\infty\) is a weighted composition operator and a criterion for \(L_\Phi\) to be isometric to \(L_\infty\) is presented.
scientific article; zbMATH DE number 1060663