Best approximation in Orlicz type spaces with peak norm structure (Q1283646)

Let \( \phi \) be an Orlicz function verifying the \( \Delta_2 \) condition at infinity and let \( L_\phi:=L_\phi[0,1] \) be the corresponding Orlicz space. For fixed \( \alpha\in (0,1] \) the authors consider an ``\(\alpha\)-peak norm'' on \( L_\phi. \) If \( f\in L_\phi \) and \( M_\phi \) is a subspace of \( L_\phi \) then one defines the set of best approximation of \(f \) by elements in \( M_\phi \) with respect to the \(\alpha\)-peak norm. The authors give sufficient conditions such that \( f \) has a unique best peak approximant in \( M_\phi. \) The paper contains many misprints.