Strictly and uniformly monotone sequential Musielak-Orlicz spaces (Q1817892)

The following results typify the contents of the paper. The notation is standard. Result 1. The following statements are equivalent for \(\mu\) nonatomic: (a) \(L_\varphi(\mu)\) is a strictly monotone space. (b) \(L_\varphi(\mu)\) is a uniformly monotone space. (c) \(\varphi>0\) and \(\varphi\) satisfies the \(\Delta_2\)-condition. Result 2. The following statements are equivalent: (a) The dominated best approximation problem with respect to closed sublattices is solvable. (b) \(\phi\) satisfies the \(\delta^0_2\)-condition. Characterizations of strict monotonicity and local uniform monotonicity with respect to \(\ell_\phi\) and \(h_\phi\) are also given.