We characterize norm-one complemented subspaces of Orlicz sequence spacesℓMequipped with either Luxemburg or Orlicz norm, provided that the Orlicz functionMis sufficiently smooth and sufficiently different from the square function. We measure smoothness ofMusingAC1andAC2classes introduced by Maleev and Troyanski in 1991, and the condition forMto be different from a square function is essentially a requirement that the second derivativeM″ofMcannot have a finite nonzero limit at zero. This paper treats the real case; the complex case follows from previously known results.
Extreme Points and Strong U-Points in Musielak–Orlicz Sequence Spaces Equipped with the Orlicz Norm