On some properties of Musielak-Orlicz spaces and their subspaces of order continuous elements (Q1203453)

Some criteria in order that \(\ell^ 1\) embeds complementably in a Musielak-Orlicz space \(L^ \Phi(\mu)\) and in its subspace \(E^ \Phi(\mu)\) of order continuous elements are given. It is also proved that every ideal \(L\) in \(L^ \Phi(\mu)\) such that \(\int_ T\Phi(x/\| x\|_ \Phi)d\mu=1\) for any \(x\in L\setminus\{0\}\) is contained in \(E^ \Phi(\mu)\).