Orlicz spaces of essentially bounded functions and Banach-Orlicz algebras (Q1067170)

There are characterized all pairs [\(\Phi\),\(\mu\) ], where \(\Phi\) is a convex Orlicz function and \(\mu\) is a \(\sigma\)-finite, positive measure, for which \(L^{\Phi}(\mu)=L^{\infty}(\mu)\) and all these pairs that \(L^{\Phi}(\mu)\) are Banach quasi-algebras (or Banach algebras) under pointwise multiplication of functions. A characterization of Orlicz spaces that are F-algebras under pointwise multiplication of functions is given too.